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.
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.
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?
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 :(
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.
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.
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.
Thanks for this instructive challenge. That is exactly how I did it.
The last example excellent.
4/(4+x)=y/(y+3)
Useful to student community.
Triangles 1 and 2 are similar. hence 4/h=b/3 >> hb = 12
This is what I found the result in 5 sec.
Rectangle length= L, width = W
4/L = W/3
Rectangle area = LW = 4 x 3 = 12
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?
Because I enjoy it
a & b are rectangle sides:
4/a = b/3, i.e. a×b = 12 = area
by similarity doing we can get our answer ...12
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 :(
12