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Answered

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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?

Sagot :

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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

Solution:

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
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