Chapter 9.4, Problem 30P

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

Area =150 $m^2$

To determine

To find the values of $x.$

Answer to Problem 30P

The required values are $x=-\frac{25}{2},12.$

Explanation of Solution

Given information: Given area of the triangle is $150m^2.$

Calculation:

Area of the triangle is $\frac{1}{2}ab=150m^2.$

  $\begin{array}{l}\frac{1}{2}x\left(2x+1\right)=150\\ x\left(2x+1\right)=300\\ 2x^2+x-300=0\\ \left(2x+25\right)\left(x-12\right)=0\end{array}$

Use the zero- product property.

  $x=-\frac{25}{2},12.$

Thus, therequired values are $x=-\frac{25}{2},12.$