Question

A rectangle with a perimeter of 96 feet has a length and width in a ratio of 15:1. What are the length and width?

Answer 1

Note that:

• 2L + 2B = 96 feet
• L:B = 15:1

Simplify the second equation to find L.

• L:B = 15:1
• => L/B = 15/1
• => L = 15B

Substitute the value of L into the first equation to find B.

• 2L + 2B = 96 feet
• => 2(15B) + 2B = 96 feet
• => 32B = 96 feet
• => B = 96/32 feet = 3 feet

Substitute the value of B into L = 15B to find L.

• L = 15B
• => L = 15(3)
• => L = 45 feet

Answer 2

l = x

w = y

x:y = 15:1

x=15y

perimeter = 2(l+w)

96 = 2(l+w)

48 = l+w

48 = x+y

48 = 15y+y

48=16y

y = 3

x = 15.3 = 45

length = 45 ft

width = 3 ft