Chapter 8, Problem 7CUR

To determine

The statement in the given question

Answer to Problem 7CUR

Ratio of the length of leg to the length of hypotenuse is $1:\sqrt{2}$

Explanation of Solution

Given information:

The given triangle is an isosceles right angle triangle.

Let x be the length of leg

By the Pythagoras theorem

  $\begin{array}{c}{\left(hypo.\right)}^2=x^2+x^2\\ {\left(hypo.\right)}^2=2x^2\\ \left(hypo.\right)=\sqrt{2}x\\ so,\frac{leg}{hypo.}=\frac{x}{\sqrt{2}x}=\frac{1}{\sqrt{2}}\end{array}$

Therefore the ratio of the length of leg to the length of hypotenuse is $1:\sqrt{2}$