Question

The length of a rectangle is 6 more than its width. The perimeter is 48 inches. What is the length?

Answer 1

`15` inches

Explanation:

Let the width be x.

Length =
`6+x`

Perimeter = Length + Length + Breadth + Breadth

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

`6+x+6+x+x+x=48`

`4x+12=48`

Subtract 12 from both sides:

`4x+12-12=48-12`

`4x=36`

Divide both sides by 4:

`(4x)/(4)=(36)/(4)`

`x=9` (Width)

Length =
`9+6=15` inches.

Answer 2

l = 15 inches

Explanation:

l = w + 6

p = 2l + 2w

substitute l into equation p

48 = 2(w + 6) + 2w

distribute the 2 into the parentheses

48 = 2w + 12 + 2w

combine like terms

48 = 4w + 12

subtract 12 from both sides

36 = 4w

divide by 4

9 = w

plug w into equation l

(9) + 6 = 15

l = 15 inches