Chapter 10.3, Problem 30P

Find the length of the hypotenuse of the right triangle to the right. Write your answer in simplified radical form.

To determine

To find: the length of the hypotenuse of the right triangle.

Answer to Problem 30P

The length of the hypotenuse of the right triangle is $x=\sqrt{14}$ .

Explanation of Solution

Given information:

The legs of the right triangle are $\sqrt{5}-\sqrt{2},\sqrt{5}+\sqrt{2}$ .

Calculation: to find the length of the hypotenuse, use the Pythagoras theorem and then simplify,

  $\begin{array}{l}{\left(x\right)}^2={\left(\sqrt{5}-\sqrt{2}\right)}^2+{\left(\sqrt{5}+\sqrt{2}\right)}^2\\ {\left(x\right)}^2=5+2-2\sqrt{10}+5+2+2\sqrt{10}\text{ [sqaure]}\\ {\left(x\right)}^2=14\text{ [simplify]}\\ x=\sqrt{14}\text{ [sqaure root]}\end{array}$

Thus, The length of the hypotenuse of the right triangle is $x=\sqrt{14}$ .