Can You Solve this MIT University Entrance Exam?

[@marioalb9726]

s² = 9 cm² -> s = 3 cm ; R =3√2 cm tanα = s/s√2 = 1/√2 --> cosα= √2/√3 x= 2R cosα= 6√2.√2/√3= 12/√3= 4s/√3 x = 4√3 cm ( Solved √ ) x = f (s) = 4/√3. s

[@ناصريناصر-س4ب]

There are two similar triangles, one of which is drawn in the semicircle and the other has one side that is the side of the square. From this we can deduce the similarity ratios: 3√2/x = 3√3/6√2, and from this x = 4√3.

[@PrithwirajSen-nj6qq]

We may draw another identical square adjacent to the given square Two square will make rectangle. The length of the rectangle is 3*2=6 It is a chord and another chord (x) is given. Now according to intersecting chord theorem ,h *(x -h) =3*3 =9 > 3√3(x -3√3)= 9 > x - 3√3 =9/3√3=√3 > x =4√3

[@paparmar]

Going through the steps, keeping the value of s open, we arrive at x = 4/3 * s * SQRT(3). Check: if s = 3, then x = 4/3 * 3 * SQRT(3) = 4 * SQRT(3). In terms of r: x = 2/3 * r * SQRT(6).

[@zawatsky]

А чего тут думать? Радиус равен диагонали, это корень из двойной площади, т. е. r=3√2. Малый треугольник выходит с катетами 3 и 3√2, его гипотенуза 3√3. Добиваем секущей слева до подобного треугольника (угол опирается на диаметр, значит прямой, а острый угол у них общий). Его гипотенуза - это диаметр, равный двум радиусам. Коэффициент подобия 2r/3√3 - пока оставим так. И на него же надо снова помножить один радиус, т. к. это ещё и больший катет. Т. е. в итоге выйдет 2r²/3√3, т. е. 36/3√3=12/√3=4*3/√3=4√3. Это в России ещё считается «внутри коробки», просто чтобы вы знали.🤭

[@heenakhandelwal8608]

3:25 x = s√3 + s/√3

[@tradefortutara9608]

How exciting😊.

[@Fujui]

Keep it up!!

[@lanoviadearana]

the best canal about maths

[@JUGNUMEHROTRANEETASPIRANT]

We , at 3:26 , answer is 4s/√(3) = x 😁

[@JUGNUMEHROTRANEETASPIRANT]

Thanks a lot Brain station for Liking (i.e. , appreciating my Answer) 😁😅

[@m.d.abdul.rahman]

एक कमरे में 5 बत्तियां जल रही हैं। अगर तुम 2 बत्तियां बुझा दो, तो कमरे में कितनी बत्तियां बची रहेंगी? विकल्प: (A) 3 (B) 5 (C) 2 (D) 0 Which option is correct comment your answer

[@JigneshGirase-v4k]

5

[@AE-DI]

3 The 2 two lights burnt off

[@youssefelyousfi4929]

x=√48 u

[@heckno3188]

How can u just asume that its the middle of the circle ?

[@toddkes5890]

I think it was stated to be the center of the circle as part of the problem being set up.

[@samdaman2510]

It is part of the problem

[@SumitVerma-lg3qh]

Easy peasy

[@MartinSun-v2q]

it's like chinese junior high school stuff😂 but we do it like this: draw a line from center that perpendicular to x we can find the radius of the semicircle is 3*SQRT(2), so 0.5x:3*SQRT(2)=3*SQRT(2):SQRT(3^2+(3*SQRT(2)^2) so x=4*SQRT(3) you can calculate like this in your head even without writing anything