Question

The perimeter of a parallelogram is 72 meters . The width of the parallelogram is 4 meters less than its length. Write an equation that could be used to find the length of the parallelogram.

Answer 1

4L = 64

Explanation: The perimeter of a parallelogram (like most other quadrilaterals) is defined as;

P = 2 (L + W)

Where P is the perimeter, L is the length and W is the width. Note that the width is given as 4 metres less than its length, hence if the length is L then the width shall be L-4. The perimeter can now be expressed as follows:

P = 2 (L + [L-4])

If the perimeter is 72, then

72 = 2 (L + L - 4)

72 = 2 (2L - 4)

By expanding the bracket on the right hand side we now have;

72 = 4L - 8

Add 8 to both sides of the equation

72 + 8 = 4L - 8 + 8

80 = 4L

Therefore the equation is 4L = 80

And the Length is 20 metres.