Question

Joe's rectangular garden is 6 meters long and 4 meters wide. He wishes to double the area of his garden by increasing its length and width by the same amount. Find the number of meters by which each dimension must be increases?

Answer 1

2 meters

Explanation:

The area of the original garden is 24 square meters. John wants to double that area to 48 square meters by increasing the length and width by the same amount.

`(6 + x)(4 + x) = 48`

`24 + 10x + {x}^(2) = 48`

`{x}^(2) + 10x - 24 = 0`

`(x + 12)(x - 2) = 0`

x + 12 = 0 or x - 2 = 0

x = -12 or x = 2

We discard the negative solution, so x = 2.

So John must increase the length and width of his garden by 2 meters.