Chapter 9, Problem 10CUR

To determine

To Find: two possible length of third side of a right − angle triangle.

Answer to Problem 10CUR

Two possible length of third side are 11.66 and 8.

Explanation of Solution

Given information: The length of two sides of a right angle triangle is 6 and 10.

Let ABC be a right − angle triangle in which AC is the hypotenuse.

Also, let $AB=6\text{ and}BC=10$ .

Using Pythagorean theorem, we get:

  $\begin{array}{c}AC=\sqrt{A{B}^2+B{C}^2}\\ =\sqrt{6^2+{10}^2}\\ =\sqrt{36+100}\\ =\sqrt{136}\\ =11.66.\end{array}$

Therefore, the length of third side is $AC=11.66$ .

Again, consider $AB=6\text{ and}AC=10$ ,

  $BC=8$ .

Therefore, the length of third sides is $BC=8$ .

Hence, the two possible lengths of the third side are 11.66 and 8.