1.3 Q8

The length of a new rectangular playing field is 6 yards longer than double the width. If the perimeter of the rectangular playing field if 282 yards, what are its dimensions?

Create a system of equation based on the problem

An expression for "the length is 6 yards longer than double the width"

⇒ l = 2w + 6 (first equation)

An expression for "perimeter is 282 yards"

⇒ 2l + 2w = 282 (second equation)

Work on the system of equation by substitution method

Substitute (2w + 6) as l, to the second equation

2l + 2w = 282

2 (2w + 6) + 2w = 282

4w + 12 + 2w = 282

6w + 12 = 282

6w = 282 - 12

6w = 270

w = 270/6

w = 45

The dimension of the field is 45 yards

Substitute the value of w, that is 45, to the first equation to find the value of l

l = 2w + 6

l = 2 (45) + 6

l = 90 + 6

l = 96

The length of the field is 96 yards