Question

The length of a rectangle is 5m longer than its width.
If the perimeter of the rectangle is 42m, find its area.

Answer 1

First, you know that the length of the rectangle is 5m longer than the width, which can be written as:
L = W + 5 (with W=width and L= length)
Secondly,you know that a rectangle has 4 sides with each of the opposite sides having the same length, and the total perimeter is 42m. So:
W+W+L+L = 42 or 2W + 2L = 42
Now you can plug the first equation into the second equation, replacing the L value:
2W + 2L = 42
2W + 2(W+5) = 42
2W + 2W + 10 = 42
4W + 10 = 42
4W = 32


W = 8
Now plug this into the first equation to find the length:
L = W + 5
L = 8+5
L = 13
So the length of the rectangle is 13m and the width is 8m.
Finally, use the area of a rectangle equation (A=L*W) to finish the problem:
A = L*W
A = 13*8
A = 104 meters squared
So the area of the rectangle is 104 meters squared.