Perimeter word problem

The formula for the perimeter of a rectangle is P = 2L + 2W. The perimeter of the local high school soccer field is 268 feet. The length is 34 ft longer than the width. Find the dimensions of the soccer field. 

Perimeter = 2(length) + 2(width)

x = width
x + 34 = length   {length is 34 ft longer than the width}

2x + 2(x + 34) = 268   {perimeter is 2(width) + 2(length)}
2x + 2x + 68 = 268   {used distributive property}
4x + 68 = 268   {combined like terms}
4x = 200   {subtracted 68 from both sides}
x = 50   {divided both sides by 4}
x + 34 = 84   {substituted 50, in for x, into x + 34}

width = 50 ft
length = 84 feet 

Ask Algebra House