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.