Question

Edwin and Anthony are building a rectangular deck in their backyard. The longer side is 2 ft more than 1/3 of the perimeter. The shorter side is 1/10 of the perimeter. They also know that the longer side is 9 ft longer than the shorter side. What is the perimeter of the deck?

Answer 1

30 ft

Explanation:

Perimeter of a rectangle = 2(length + width)

Let

Perimeter = x

Length = 1/3x + 2

Width = 1/10x

Length = 9 + 1/10x

Perimeter of the deck = 2(length + width)

x = 2(1/3x + 2 + 1/10x)

x = 2(10x+3x/30 + 2)

x = 2(13/30x + 2)

x = 26/30x + 4

x - 26/30x = 4

30x-26x/30 = 4

4/30x = 4

Divide both sides by 4/30

x = 4 ÷ 4/30

= 4 × 30/4

x = 30 ft

Length = 1/3x + 2

= 1/3(30) + 2

= 30/3 + 2

= 10 + 2

= 12 ft

Width = 1/10x

= 1/10(30)

= 30/10

= 3 ft

Length = 9 + 1/10x

= 9 + 1/10(30)

= 9 + 30/10

= 9 + 3

= 12 ft

The perimeter of the deck = x = 30 ft