Question

The length of a rectangle is 4 inches more than twice the width. If the area the rectangle is 48 square inches, what is the length of the rectangle ?

Answer 1

The length of the rectangle is 12 inches.

Explanation:

Let the length and width of the rectangle be represented as l and w respectively.

Thus,

l = 2w+ 4

area = 48 square inches

So that,

Area of a rectangle = l x w

48 = (2w + 4) x w

= 2
`w^(2)` + 4w

2
`w^(2)` + 4w - 48 = 0

Divide through by 2 to have;

`w^(2)` + 2w - 24 = 0

(
`w^(2)` - 4w) (6w - 24)

w(w - 4) + 6(w - 4)

Thus,

(w - 4) or (w + 6)

w - 4 = 0 or w + 6 = 0

w = 4 or w = -6\

Therefore, the width of the rectangle is 4 inches. Then,

length, l = 2w + 4

= 2 (4) + 4

= 12 inches

The length of the rectangle is 12 inches.