Question

Find the diagonal of 9 inche square?

Answer 1

First, picture a square that naturally has all sides equal to each other. If you draw a diagonal across, you realize a square is just 2 right triangles put together. Because all sides are equal, we can assume that these are special triangles. In particular, a 45, 45, 90 degree triangle. The diagonal is just the hypotenuse.

So for a 45, 45,  degree triangle, the sides are as follows:  x, x , and $x\sqrt{2}$  .

So the sides would be 9, 9, $9\sqrt{2}$ (this can't be simplified)

Your answer is $9\sqrt{2}$