Don L. answered • 02/10/20

Fifteen years teaching and tutoring basic math skills and algebra

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

p_{1} = 2(x + 4) + 2 *9

p_{1} = 2x + 8 + 18, or 2x + 26

Perimeter of second rectangle:

l = x

w = 6cm

p_{2} = 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?