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

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

Base =
`(2x^2+(10x+3x)+15)/(2x+3)`

Base =
`(2x(x+5)+3(x+5))/(2x+3)`

Base =
`((2x+3)(x+5))/(2x+3)`

Base =
`x+5`

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