Question

In a 45-45-90 triangle, the ratio of the length of the hypotenuse to the length of a side is

Answer 1

Explanation:

See the figure below for a better understanding of the problem. Since we have a 45-45-90 triangle, this is an isosceles triangle, so both the adjacent and opposite sides measure the same value, say, x. Then the hypotenuse would be:

$H=\sqrt{x^2+x^2} \\ \\ H=2\sqrt{2}$

Then. the ratio of the length of the hypotenuse to the length of a side is:

$\boxed{r=\frac{2\sqrt{x}}{x}}$