Question

A parallelogram has a base of length `2x+1`, a height of `x+3`, and an area of 42 square units. What are the base and height of the parallelogram?

Answer 1

Base is 7, Height is 3.

Explanation:

The area of any parallelogram is Length x Width (Which is sometimes called height, depends on the textbook). We know that the length is `2x+1` and the Width (AKA Height) is `x+3` so we put them into an expression following Length x Width = Area and solve to get x=3. We then plug it into each equation to get 7 for the base and 6 for the height.

Answer 2

length = `2(3) + 1` = 7
height = `(3) + 3` = 6

Explanation:

`Area = base xx height`

`(2x+1)(x+3) = 42`

`2x^2 + 6x + x + 3 - 42 = 0` [make quadratic = 0]

`2x^2 + 7x - 39 = 0` [factorise]

`(2x +13)(x-3) = 0`

`x = -6 1/2` or `x =3`

Reject `-6 1/2` because a side cannot be negative.

`x = 3`