Chapter 8.3, Problem 36PPS

To determine

To write: The expression which represents the area of the triangle.

Answer to Problem 36PPS

  $3x^2+\frac{7}{2}x-\frac{3}{2}$

Explanation of Solution

Given:

Base of the triangle is $2x+3$ and height is $3x-1$

Calculation:

The area of the triangle is given by

  $\begin{array}{l}\frac{1}{2}\cdot \text{base}\cdot \text{height}\\ \text{=}\frac{1}{2}\cdot \left(2x+3\right)\left(3x-1\right)\\ =\frac{1}{2}\left(6x^2-2x+9x-3\right)\\ =\frac{1}{2}\left(6x^2+7x-3\right)\\ =3x^2+\frac{7}{2}x-\frac{3}{2}\end{array}$

Therefore, the expression that represents the area of the triangle is $3x^2+\frac{7}{2}x-\frac{3}{2}$