Question

The length of a rectangle is 6 in. more than the width. The perimeter of the rectangle is 24 in. Find the dimensions of the rectangle.

Answer 1

1. First, let us define the width of the rectangle as w and the length as l.

2. Now, given that the length of the rectangle is 6 in. more than the width, we can write this out as:

l = w + 6

3. The formula for the perimeter of a rectangle is P = 2w + 2l. We know that the perimeter of the rectangle in the problem is 24 in. so we can rewrite this as:

24 = 2w + 2l

4. Given that we know that l = w + 6, we can substitute this into the formula for the perimeter above so that we will have only one variable to solve for. Thus:

24 = 2w + 2l

if l = w + 6, then: 24 = 2w + 2(w + 6)

24 = 2w + 2w + 12 (Expand 2(w + 6) )

24 = 4w + 12

12 = 4w (Subtract 12 from each side)

w = 12/4 (Divide each side by 4)

w = 3 in.

5. Now that we know that the width is 3 in., we can substitute this into our formula for length that we found in 2. :

l = w + 6

l = 3 + 6

l = 9 in.

6. Therefor the rectangle has a width of 3 in. and a length of 9 in.