Question

Melissa wants to expand her rectangular sandbox that measures 4 feet by 8 feet. Two sides of the sandbox are against a fence. She wants to increase the length and the width of the sandbox by the same amount on the two sides that are not against the fence. The total area of the new sandbox will be 60 square feet. What is the amount of increase?

Answer 1

Answer:

The amount with which she should increase the length and the with of the sandbox is 2 feet each

Step-by-step explanation:

The dimensions of Melissa's rectangular box are;

Width of the box = 4 feet

Length of the box = 8 feet

The total area of the new sandbox, A = 60 square feet

Let 'x' represent the amount by which she increases the width and lengths of sides that not against the fence, we have;

The area of the new sandbox, A = The new length × The new width

A = 60 ft.²

The new length = 8 + x

The new width = 4 + x

∴ A = 60 = (8 + x) × (4 + x) = x² + 12·x + 32

60 = x² + 12·x + 32

60 - 60 = 0 = x² + 12·x + 32 - 60

∴ x² + 12·x - 28 = 0

(x + 14)·(x - 2) = 0

x = -14 or x = 2

Therefore, the amount she can increase the width and lengths of sides that not against the fence to have make a new sandbox with an area of 60 ft.² is, x = 2 feet

The amount of increase of the length and the width of the sandbox, x = 2 feet each.