Answer:
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
