The length of a rectangle is 6 m longer than its width.
If the perimeter of the rectangle is 32 m, find its area.

55m^2

Step-by-step explanation:

The area of a rectangle is l x w (width x height)

We know that the length (l) of the rectangle is 6m longer than its width (w), then:

(1) l = w + 6

We also know that the perimeter of the rectangle is 32m, so:

(2) 2l + 2w = 32

Now substitute the value of l in (1) for l in (2):

2(w + 6) + 2w = 32

Distribute:

2w + 12 + 2w = 32

Combine like terms and subtract 12 from both sides:

4w = 20

Divide both sides by 4:

w = 20/4 = 5 (so the width is 5m)

Find the length (use (1)):

l = 5 + 6 = 11m (length of rectangle)

Then, the area is:

A = l x w = 5 x 11 = 55m^2