Question:

The length of a rectangle is two less than three times the width. If the perimeter of the rectangle is 76 cm, find the dimensions of the rectangle.

Solution:

A diagram is particularly useful in a problem of this kind. A rectangle is four-sided figure in which the opposite sides are equal and the sides meet at right angles. Thus, for a rectangle.

• P = 2a + 2b

In our problem we are told that the length is two less than three times the width. Since the length is described in terms of the width we can let

• w = width of the rectangle

Then 3w - 2 = length of the rectangle (length is 2 less than 3 times the width).

Alternatively, we could simply draw a diagram and label it as shown in the diagram.

• (Attached photo)

The perimeter being 76 cm gives us the equation

• 2w + 2(3w - 2) 76
• 2w + 6w - 4 = 76
• 8w = 80/8
• w = 10

If the width is 10 cm, then the length is

• 3w - 2 = 3(10) - 2 = 28 cm

Checking of the solution to the word problem is left to the students

Answer:

• The dimensions of the rectangle are w = 10 cm and l = 28 cm.