The area of a rectangular wall of a barn is 16 square feet. It’s length is 4 feet longer than twice it’s width find the length and width of the wall of the barn

Answer 1

Hi Judyth,

Let's use the variable w to represent the width of the wall. We can write the following expression to represent the length: 2w + 4

Then area is calculated by multiplying the length by the width. Here that would be:

A = length • width

16 = (2w + 4 ) • w

16 = 2w² + 4w

This can be solved for w using factoring as follows:

16 = 2w² + 4w

16 - 16 = 2w² + 4w - 16

0 = 2w² + 4w - 16

0 = 2 (w² + 2w - 8)

We can factor this as 0 = 2(w +4 ) (w - 2)

Since the width can't be a negative number, w would be 2 feet.

The length would be 2w + 4 OR 2 • 2 + 4 = 8 feet

The length would be 8 feet.

To verify the area:

A = 8 • 2 = 16 feet ²