Question

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square. Determine the missing side length .

Answer 1

Lets draw the following picture:

From the figure, we can see that the area of the square on the left is given by

$a^2=225$

And the area of the square below is

$b^2=8^2=64$

By applying Pytagorean theorem,

$a^2+b^2=c^2$

we get

$225+64=c^2$

which gives

$c^2=289$

therefore, c is equal to

$c=\sqrt[]{289}$

and the answer is c = 17.