Question

A parallelogram with a height of 2x+3 has an area of 2x^2+13x+15. What is the length of the base of the parallelogram? Please show work.

Answer 1

(2x^2+13x+15)/2x+3=x+5

Use long or synthetic division to solve this problem.

Answer 2

Answer : The length of the base of the parallelogram is, $x+5$

Step-by-step explanation :

As we know that:

Area of parallelogram = Height × Base

Given:

Height of parallelogram = $2x+3$

Area of parallelogram = $2x^2+13x+15$

Now put all the given values in the above formula, we get:

Area of parallelogram = Height × Base

$2x^2+13x+15$ = $2x+3$ × Base

Base = $\frac{2x^2+13x+15}{2x+3}$

Now factorize this expression $2x^2+13x+15$, we get:

Base = $\frac{2x^2+(10x+3x)+15}{2x+3}$

Base = $\frac{2x(x+5)+3(x+5)}{2x+3}$

Base = $\frac{(2x+3)(x+5)}{2x+3}$

Base = $x+5$

Therefore, the length of the base of the parallelogram is, $x+5$