Chapter 7.7, Problem 83STP

To determine

To Find :

A simplified expression for the measure of the hypotenuse.

Answer to Problem 83STP

  $4x^2{y}^2\sqrt{5}$

Explanation of Solution

Given Information:

The measures of the legs of a right triangle can be represented by the expressions $$

  $4x^2{y}^2\text{ and }8x^2{y}^2$ .

Calculation:

  $\begin{array}{l}Given\\ a=4x^2{y}^2\\ b=8x^2{y}^2\\ c=hypotenuse=\sqrt{a^2+b^2}\\ \Rightarrow c=\sqrt{{\left(4x^2{y}^2\right)}^2+{\left(8x^2{y}^2\right)}^2}\\ \Rightarrow c=\sqrt{16x^4{y}^4+64x^4{y}^4}\\ \Rightarrow c=\sqrt{16x^4{y}^4(1+4)}\\ \Rightarrow c=4x^2{y}^2\sqrt{5}\\ \text{Hence, the measure of the hypotenuse is }4x^2{y}^2\sqrt{5}\end{array}$