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kotegsom [21]
3 years ago
5

A building in a city has a rectangular base. The length of the base measures 65 ft less than twice the width. The perimeter of t

his base is 770 ft. What are the dimensions
of the base?
Mathematics
1 answer:
Reika [66]3 years ago
8 0

Answer:

  • 235 ft long
  • 150 ft wide

Step-by-step explanation:

In order to find two unknown values, length and width of a rectangle, you must have two independent relations between those values. One relation is given in the problem statement:

  L = 2W -65 . . . . . length is 65 ft less than twice the width

Another relation is given by the formula for the perimeter of a rectangle:

  P = 2(L +W) . . . . with P = 770 given in the problem statement

__

Using the first relation for L, we can substitute into the relation for perimeter to get ...

  770 = 2((2W -65) +W)

  770 = 6W -130 . . . . . . . . simplify

  900 = 6W . . . . . . . . . add 130 to both sides

  150 = W . . . . . . . . divide both sides by 6

  L = 2(150) -65 = 235 . . . . . use the equation for L to find the length

The base is 235 feet long and 150 feet wide.

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