Question

Use an algebraic equation to solve the problem.

A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary.

Responses:

a) 7.5 cm by 22.5 cm

b) 7.5 cm by 52.5 cm

c) 20 cm by 60 cm

d) 15 cm by 22.5 cm

Answer 1

Let the width of the rectangle be x cm. Therefore, the length of the rectangle is 3x cm.

The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)

Substituting the values into the formula:
60 = 2(3x + x)

Simplifying the equation:
60 = 2(4x)
30 = 4x
x = 7.5

Therefore, the width of the rectangle is 7.5 cm, and the length is 3 times that, which is 22.5 cm.

The correct answer is a) 7.5 cm by 22.5 cm