The area of two rectangles is 360 square centimeters.

Question

The length of the second rectangle is 12 cm greater than the first while its width is

 5 cm less than the first. Find the difference of the perimeters of the two rectangles if the lengths and widths are positive integers.

 

Answer 1

Length of the first rectangle = x

Then length of second rectangle = x + 12

Width of first rectangle = y

Then width of second rectangle = y - 5

Perimeter of first rectangle(P₁) = 2(x + y)

P₁ = 2x + 2y

Perimeter of second rectangle(P₂) = 2(x + 12 + y - 5)

= 2x + 24 + 2y - 10

P₂ = 2x + 2y + 14

Difference = P₂ - P₁

= (2x + 2y + 14) - (2x + 2y)

= 2x + 2y + 14 - 2x - 2y

= 14

Difference of the perimeters is 14 cm.