Question

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

Answer 1

Step-by-step 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=√(x^2+x^2) \\ \\ H=2√(2)`

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

`\boxed{r=(2√(x))/(x)}`