Can you solve the Logic Puzzle? | Find area of Blue Rectangle | (Easy explanation) |

[@luckshmana3461]

Sir, I love your stuff and please don't stop making these videos

[@PreMath]

Thank you, I will! You are awesome. Keep it up 👍

[@michaelkouzmin281]

one more solution: let the length of the blue rectangle be x and its height - y; then {(x-9)*(6-y)=12 and (x-8)*(8-y)=24} 2 solutions (1) x= 12; y= 2 AreaBlue = 24 (looks nice); (2)x=11, y=0, Area = 0 - we have no other choice as to reject it.

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@williamwingo4740]

Here's a more algebraic approach: Let x be the width of the yellow rectangle and y the height of the blue rectangle. Then the width of the green rectangle = x + 1, as you explain at 2:10 in the video. Now calculating the areas of the upper and lower auxiliary rectangles: yellow: (x)(6 - y) = 12; multiplying out, 6x - xy = 12; call this equation 1. green: (x + 1)(8 - y) = 24; multiplying out, 8x - xy + 8 - y = 24; subtracting 8 from both sides, 8x - xy - y = 16; call this equation 2. Now subtract equation 1 from equation 2 to get rid of the xy term. We get: [8x - xy - y = 16] - [6x - xy = 12] ----------------------------- 2x - y = 4. Solve this for y in terms of x; and y = 2x - 4. We now plug this value for y back into equation 1 (because it's simpler than equation 2): 6x - (x)(2x -4) = 12; multiplying out, 6x - 2x^2 + 4x = 12; collecting terms and rearranging, - 2x^2 + 10x - 12 = 0; dividing through by -2, x^2 - 5x + 6 = 0; this quadratic can be factored by inspection (thanks to Miss Whaley in 1963): (x - 3)(x - 2) = 0; so x = either 2 or 3. We reject the x = 2 solution because y = 2x - 4 and this would make y = 0. Therefore x = 3 and y = 6 - 4 = 2. And finally, the area of the blue rectangle is (y)(9 + x) = (2)(9 + 3) = (2)(12) = 24. And there's a huge pile of scratch paper on the floor. Cheers. 🤠

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@tombufford136]

A quick glance at this, although this is a first Guess, 24 = 6 * 4 and 12 = 4 * 3 giving the blue Rectangle as 12 * 2 = 24 units.

[@yalchingedikgedik8007]

That’s nice and enjoyable Thanks Sir for explain My Regards .

[@abstragic4216]

Let blue rectangle be w wide and h high, yellow rectangle area : (w-9)(6-h)=12, green rectangle area : (w-8)(8-h)=24. Solve these two simultaneous equations to give h-2 and w=12.

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@gelbkehlchen]

Solution: I call the short side a of the blue rectangle and the long side b. Then 2 equations: (1) (b-9)*(6-a) = 6b-ab-54+9a = 12 (2) (b-8)*(8-a) = 8b-ab-64+8a = 24 (2)-(1) = (3) 2b-10-a = 12 |+10+a ⟹ (3a) 2b = a+22 |/2 ⟹ (3b) b = a/2+11 |in (2) ⟹ (2a) (a/2+11-8)*(8-a) = (a/2+3)*(8-a) = 4a-a²/2+24-3a = -a²/2+a+24 = 24 |-24 ⟹ (2b) a-a²/2 = a*(1-a/2) = 0 |either a=0, but that cannot be, or 1-a/2 = 0 |+a/2 ⟹ a/2 = 1 |*2 ⟹ a = 2 |in (3b) b = 1+11 = 12 ⟹ area of the blue rectangle = 2*12 = 24

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@ybodoN]

If the width of the blue rectangle is a, then its length is 24 / (8 − a) + 8 = 12 / (6 − a) + 9 ⇒ a = 2 So, the width of the green rectangle is 24 / (8 − 2) = 4 and the length of the blue rectangle is 12 Or the width of the yellow rectangle is 12 / (6 − 2) = 3 and the length of the blue rectangle is 12 In both case, the area of the blue rectangle turns out to be 2 × 12. So the final answer is 24 cm²

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@ronaldreygalos]

let x=width of the blue rectangle y=width of the yellow rec z=width of green rec Sol: (6-x)y=12 eq1 ( 8-x)z=24 eq2 9+y=8+z, z=y+1 eq 3 Substitute eq 3 to 2 (8-x)(y+1)=24 8y+8-xy-x=24 8y-xy-x=16 y(8-x)-x=16, substitute eq1 (12/6-x)(8-x)-x=16 12(8-x)-x(6-x)=16(6-x) 96-12x-6x+x^2=96-16x -18x+x^2+16x=0 x^2-2x=0 x(x-2)=0 x=0, x=2 thus x=2 since we r computing the measurement substitute x to eq 1 (6-2)y=12 4y=12 y=3 then substitute to the length L=9+y=9+3=12 thus, L=12 and width 2 compute the area of the blue rec A=LW=12•2 A=24 cm^2

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@HappyFamilyOnline]

Great explanation 👍 Thanks for sharing 😊

[@PreMath]

My pleasure 😊 You are awesome. Keep it up 👍

[@devondevon4366]

24 Let the width of the yellow = n and its length =p Hence area is np=12 Equation 1 or p = 12/n Equation 2 Since 9 + the Width of the Yellow = length of the Blue, but 8 + the Width of the Green = length of the Blue, then the Width of the Green is 1 unit greater than the width of the Yellow. Hence width of the Green = n+1 Since the length of the Yellow + the Width of the Blue = 6, but the Length of the Green + the Width of the Blue =8, then the Length of the Green is 2 units greater than the Length of the Yellow Hence the length of the Green = p+2 Hence area of the Green is (n+1)(p+2) =24 2n + p+2+np =24 2n + p + 2 +12 = 24 (substitute 12 for np . see Equation 1) Hence 2 n+ p = 24-14 2n + p = 10 p = 10- 2n 12/n = 10 - 2n (substitute the value for p . See Equation 2) 12 = 10n- 2n^2 ( multiply both sides by n) 6 = 5n - n^2 ( divide both sides by 2) n^2-5n +6 = 0 (n-2)(n-3) n=2 and n=3 The width of the yellow is either 2 or 3. If 2, then the length of yellow = 6 (12/2), But the length of yellow + the width of blue = 6 Hence n =3, the width of the yellow rectangle, and its length = 4 Hence length of blue = 9+3 =12 and width of blue = 6-4 = 2 Area of blue = 12 * 2 = 24

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@dlynn101]

I got 24 by factoring the 24 from the green rectangle: 12, 8, 6, 2, 3, 4. The correct factors must be < 8. 12, 2, 8, 3 cancel, leaving 6 x 4. The blue rectangle: W = 8+4, L = 2. 12 x 2 = 24 cm2.

[@montynorth3009]

Let height of yellow rect. be x, its width y. Height of green rect. will be (x+2), its width (y+1). Yellow rect., xy = 12. y = 12/x. Green rect., (x+2) (y+1) = 24. Substitute y = 12/x. (x+2) (12/x +(1) = 24. Expanding, 12 + (24/x) + x + 2 = 24. (24/x) + x = 10. Multiply both sides by x & rearrange. x^2 - 10x + 24 = 0. Factorising. (x - 6) (x - 4) x = 6 or 4. Can't be 6, therefore 4 = height of yellow rect. Width of yellow rect.= 12/4 = 3. Height of blue rect.= 6 - 4 = 2 Width of blue rect.= 3 + 9 = 12. Area blue 12 * 2 = 24.

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@KAvi_YA666]

Thanks for video.Good luck sir!!!!!!!!!!!

[@andrevandermerwe1935]

You going the loooong way around!! Straight away you can deduce that the small side of the blue rectangle is 2.(length 8 on lhs of total figure minus 6 on rhs of figure). That gives 6 for long side of green rectangle and 4 for short side of green (6x4=24cm sq) The bottom length of blue rectangle will be this 4 + 8 which is given = 12 and the answer is 12x2 which is 24. Much more simple!!

[@dlynn101]

this was my approach

[@batavuskoga]

I could solve it in a different way. green rectangle x=height 24/x=length blue rectangle 8-x=height yellow rectangle x-2=height yellow rectangle : height=6-(8-x)=x-2 Then the middle part of the blue rectangle as shown in the video length=9-24/x and also 8-12/(x-2) 9-24/x=8-12/(x-2) When you solve this correctly with the denominator = x(x-2) you will get x²-14x+48 solving this quadratic equation you will get two solutions : x=8 and x=6 x=8 is not possible, the height of the blue rectangle will be zero (see above) x=6 is the only solution When you fill in x, you will find length blue rectangle = 12 width = 2 area blue rectangle = 12 * 2 = 24 cm²

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@SaadmaanMahmidShoshi]

I took the width of the blue rectangle. I considered it as a. So width of green rectangle becomes 24/(8-a). Similarly, width of yellow rectangle becomes 12/(6-a). Now the length of blue rectangle is actually 24/(8-a) + 9 = 12/(6-a) + 8. Solving this for a, we get a = 0 or a = 2. Obviously a = 2. Putting the value of a in either of the above expressions we get the length of the blue rectangle as 24/(8-2) + 8 = 12. Area of blue rectangle then becomes 12 × 2 = 24 sq cm. 😊

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@misterenter-iz7rz]

Let ab be the area, 8+24/(8-a)=b= 9+12/(6-a), thus 24/(8-a)-12/(6-a)=1, 24(6-a)-12(8-a)=(8-a)(6-a), a^2-2a=0, so a=2, b=8+4=12, therefore the area is 24.😊

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@syedali9914]

Sir, How did you get the area of the small leftmost blue triangle equal to x +1 ? Thanks

[@arachan31]

I think you mean the length? I was stuck on this too for a bit scratching my head. The length of the middle blue rectangle would be “8 - x”. To find the left blue rectangle*(edit) length that would be : 9 - ( 8 - x ) which would simplify to x + 1. Perhaps there’s a better way to jump to that (x + 1 ) in your head, but that’s how I figured it out.

[@shango6164]

@@arachan31 Thanks for that. I was stuck on that as well, but with your explanation, it does make logical sense now.

[@MarieAnne.]

My solution: Yellow rectangle has width = x, height = y Blue rectangle has width = 9+x, height = 6−y Green rectangle has width = (9+x)−8 = x+1, height = 8−(6−y) = y+2 Area of yellow rectangle: xy = 12 Area of green rectangle: (x+1)(y+2) = 24 xy + 2x + y + 2 = 24 12 + 2x + y + 2 = 24 2x + y = 10 2x + 12/x = 10 2x^2 + 12 = 10x x^2 − 5x + 6 = 0 (x − 2) (x − 3) = 0 x = 2, y = 6 or x = 3, y = 4 Area of blue rectangle: (9+x)(6−y) = (9+2)(6−6) = (11)(0) = 0 or (9+x)(6−y) = (9+3)(6−4) = (12)(2) = 24 So assuming a non-degenerate rectangle, we get area = 24

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@steveschooler5840]

I have seen similar videos that resulted in a result analagous to the area of the blue rectangle being 0. Also, there is the message at the beginning of the video that the drawing is "not to scale". So, I don't think the alternate solution of blue area = 0 can be validly rejected.

[@parthtomar6987]

Nice solution sir I gave you 100th like

[@PreMath]

Thanks for liking You are awesome. Keep it up 👍

[@giuseppemalaguti435]

9+12/(6-h)=8+24/(8-h)...h=2...A=bh=[9+12/(6-2)]*2=12*2=24

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@devindermehta5577]

Nice approach I took a different approach Assuming width of blue rectangle as x Then rest is all easy

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@devindermehta5577]

@@PreMath Need to talk to you. Is it possible?

[@PreMath]

@@devindermehta5577 Please send an email to [e-mail] Cheers

[@ketrin-fz8be]

If one makes the lazy assumption that the 12 cm^2 rectangle is 3cm horizontal x 4cm vertical, then the rest of the measurements fall rapidly into place.

[@arnavkange1487]

Sir how much time it requires for u to make one sum approximately

[@PreMath]

It takes enormous amount of time for research and planning to prepare quality videos! Thanks for asking

[@swastikizhere]

24 cm^2 cuz...Breadth is 8-6=2 And from the green rectangle...we can observe that 6*4=24 cm^2 ...thus total length is 4+8=12 12*2=24cm^2 (blue rectangle) I wrote the comment as I still didn't watch the vdo...

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@trannghia400]

Nhanh. Gọn.

[@wackojacko3962]

I like Golden Rectangles! More fun too play with. 🙂

[@PreMath]

Excellent! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@じーちゃんねる-v4n]

height of blue=h 9+12/(6-h)=8+24/(8-h)

[@alexniklas8777]

A=24 cm^2

[@user-jm7cx5zc9s]

There some mistake in the explanation. The ratio of area of two rectangles can't fix the horizontal lengths but only gives the ratio of horizontal lengths. thanks

[@waheisel]

I think you are correct. Premath establishes that the ratio of the width of the green rectangle to the width of the yellow rectangle is 4/3, not that the green width is 4cm nor the yellow width is 3 cm. Those dimensions are correct but I don't think he actually proved that.

[@alexandrsavely3367]

There are 2 solution for blue rectange: { w = 12 , h = 2} and { w = 11, h =0 }

[@sunitagupta7783]

Hello sir! I am a maths' student and I want to earn money so can you Please suggest me something which relate to maths only?

[@viktorkovacs9680]

A/B=a/b=8/6 then a=4 and b=3. Why? Why not 8 and 6? Or 2 and 1.5?

[@JSSTyger]

24

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@thomakondaciu6417]

S=2×12=24

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@misterenter-iz7rz]

0 or 24.

[@Brognard]

Я хз, зачем всё это расписовать Ответ приходит за секунд 15, просто посмотрев на картинку

[@cristianaliu8939]

The explanation of the problem is wrong. When you simplify with (x-2) you need to check what happened when x=2 (in this case you will have another solution and the area of the "blue rectangle" is zero)!!!

[@johndemeen5575]

Why? No one cares.

[@PreMath]

Welcome aboard, John❤️

[@johndemeen5575]

@@PreMath Mr. Muller. 5 grade, Como Lake Elementary 1966, installed a vast resentment toward mathematics. No offense intended. St.Paul,Minnesota.

[@devondevon4366]

24