Find the area of the shaded rectangle

Find the area of the shaded rectangle.
math u teach math

[@luminiferous1960]

Before watching this video, my solution is as follows: With the long side of the gray rectangle being of length x and the short side of the gray rectangle being of length y, by the laws of similar triangles, we have 4/x = y/3 Multiplying both sides by x yields: 4 = x*y/3 Multiplying both sides by 3 yields: x*y = 12 The Area of the gray rectangle is given by x*y, therefore, the answer is Area = 12.

[@williamBryan-k2e]

when I see a problem like this - I try to get h and w and then go for h*w. I could not answer this question based on that. Good method.

[@AmyRogers-h6r]

I used the “3, 4, 5” trick to do it in my head. If one side of a right triangle is 3 or 4, the hypotenuse is 5 as 9 + 16 is 25. The height is 4 and the base is 3, so the area is 12.

[@malininagaraj8248]

The last example excellent.

[@davidbrown8763]

Thanks for this instructive challenge. That is exactly how I did it.

[@cyruschang1904]

Rectangle length= L, width = W 4/L = W/3 Rectangle area = LW = 4 x 3 = 12

[@jmlfa]

Triangles 1 and 2 are similar. hence 4/h=b/3 >> hb = 12

[@madhabsikder9670]

This is what I found the result in 5 sec.

[@xdadevelopers3631]

4/(4+x)=y/(y+3)

[@plamenpenchev262]

a & b are rectangle sides: 4/a = b/3, i.e. a×b = 12 = area

[@KipIngram]

Let the rectangle have height h and width w. Write the tangent of the angles at the right tip of the triangle and the top right corner of the rectangle are similar. Write the tangent twice: tan(angle) = h/3 = 4/w w*h = 12 So the area is 12. Q.E.D. Um, how could you have spent five minutes on this?

[@mathu6514]

Because I enjoy it

[@Uma-Bharat-India]

Useful to student community.

[@xdadevelopers3631]

by similarity doing we can get our answer ...12

[@kelly4187]

This is what I did. 4/x = y/3, so y=12/x, so area is 12. I had hoped it wouldn’t be a 12 second problem. I had hoped it was one that would look simple but be tricky :(

[@nenetstree914]

12