Chapter 8.6, Problem 39P

A parallelogram has an area of $4x^2+7x-15.$

The base of the parallelogram is $x+3.$

What is the height of the parallelogram?

a. Write the formula for the area of a parallelogram.

b. Writing Explain how factoring the trinomial helps you solve the problem.

To determine

To write the formula for the area of a parallelogram.

Answer to Problem 39P

Area of the parallelogram with base b and height h is,

  $A=b\times h$

Explanation of Solution

Area of the parallelogram with base b and height h is,

  $A=b\times h$

To determine

To determine how factoring the trinomial helps to solve the height of the parallelogram.

Answer to Problem 39P

height is $\left(4x-5\right)$

Explanation of Solution

Given information :

Area of parallelogram is given $4x^2+7x-15$

Area of the parallelogram with base b and height h is,

  $A=b\times h$

Here we shall observe that the area is product of two factors, base and height.

Therefore we may find height of the parallelogram by factoring the expression for area.

Hence we factor the expression for area.

We get,

  $\begin{array}{c}4x^2+7x-15=4x^2+12x-5x-15\\ =4x\left(x+3\right)-5\left(x+3\right)\\ =\left(4x-5\right)\left(x+3\right)\end{array}$

We know that $\left(x+3\right)$ is base. Therefore height is $\left(4x-5\right)$