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

Question

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

Answer 1

Anda,

 

Since the area of the rectangle is l * w, we need to find both.

 

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 * w = 5 * 11 = 55m²

 

Hope this helps!