Question

When three squares are joined at their vertices to form a right triangle, the combinedarea of the two smaller squares is the same as the area of the largest square.Which three squares do NOT support this statement?34 in10 in.Aс3 in24 in.26 in.5 in225 in 21681 in 2BD1600 in 28 in16 in.9 in

Answer 1

We need to study in each case the relationship given by the pythagorean theorem, which states: a^2 + b^2 = hypotenuse^2

First image (A):

The square's areas are:

34 , 3^2 and 5^2 . That is: 34 , 9 and 25

when we add 9 + 25 = 34

so the theorem holds true.

Second image(B):

225, 8^2, and 16^2 . That is: 225, 64, and 256

we notice that 225 + 64 = 289 which is NOT 256. So this case is FALSE.

Third image (C):

Areas : 10^2, 24^2 and 26^2 . That is: 100, 576, and 676

we notice that 100+ 576 = 676, so the relationship holds true.

Fourth image (D):

1600, 1681 and 9^2 That is: 1600, 1681, and 81

we notice that 1680 + 81 1681, then the relationship holds true.

The FALSE one is figure B.