Question

The chicken coup at the petting farm is 10 by 14 feet. The farm would like to double the current area

by adding the same amount, x, to the length and width. What are the dimensions of the new
enclosure? Round to the nearest hundredth of a foot.

Answer 1

14.85 feet & 18.85 feet

Explanation:

This is a rectangle with area 10 * 14 = 140 sq. ft.

We want new rectangle to be DOUBLE this area, so that area would be:

140 * 2 = 280 sq. ft.

We will add same amount, x, to both length and width, to get 280. Lets do this and find x. [note: length * width = area]

Area = length * width

280 = (10+x)*(14+x)

280 = 140 + 10x + 14x + x^2

0 = -140 + 24x + x^2

We can solve this by using middle term factorization:

`x^2+24x-140=0\\x=4.85`

So, we need to add around 4.85 feet to both length and width

New dimensions are 14.85 feet & 18.85 feet