Chapter 9.4, Problem 29P

Find the value of $x$ as it relates to each rectangle or triangle.

Area = 20 $in{.}^2$

To determine

To find the values of $x.$

Answer to Problem 29P

The required values are $x=-8,5.$

Explanation of Solution

Given information: Given area of the triangle is $20i{n}^2.$

Calculation:

Area of the triangle is $\frac{1}{2}ab=20i{n}^2.$

  $\begin{array}{l}\frac{1}{2}x\left(x+3\right)=20\\ x^2+3x=40\\ x^2+3x-40=0\\ \left(x+8\right)\left(x-5\right)=0\\ x=-8,5.\end{array}$

Use the zero- product property.

  $x=-8,5.$

Thus, the required values are $x=-8,5.$