Word Problem to an Algebraic Equation

Question

Presley has just drawn two rectangles. The length of the first rectangle is 4cm more than the length of the second. The width of the first is 9cm; the width of the second is 6 cm. The COMBINED perimeters is the same as three times the perimeter of the second rectangle. What is the length of the second rectangle?

Answer 1

Hi Suhas, let x represent the length of the second rectangle. Then x + 4 represent the length of the first rectangle.

Formula for perimeter of a rectangle:

p = 2l + 2w

Perimeter of first rectangle:

l = x + 4

w = 9cm

p₁ = 2(x + 4) + 2 *9

p₁ = 2x + 8 + 18, or 2x + 26

Perimeter of second rectangle:

l = x

w = 6cm

p₂ = 2x + 2 * 6, or 2x + 12

Given sum of the perimeter of first rectangle plus second rectangle is equal to three times the perimeter of the second rectangle.

Sum of first rectangle plus second rectangle:

2x + 26 + 2x + 12

4x + 38

Three times perimeter of second rectangle:

3 * (2x + 12), or 6x + 36

Then:

4x + 38 = 6x + 36

Combine terms:

2x = 2

x = 1

The length of the second rectangle is 1 cm.

The length of the first rectangle is x + 4, or 1 + 4 = 5 cm.

Questions?