Question

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 this base is 770 ft. What are the dimensions
of the base?

Answer 1

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.