Word problem to figure base width and length in feet.

Question

A building has a rectangular base. The length of the base measures 75 feet less than twice the width. The perimeter of this base is 870 feet. What are the dimensions of the base. Width of base is ___ feet  and length of base is ____ feet?  Show formula used to find answer. 

Answer 1

Hi Tony, let W be the width of the base. Then 2W - 75 will be the length of the base.

 

Use the formula for the perimeter of a rectangle: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

 

Substitute:

 

P = 870 feet

 

L = 2w - 75

 

Equation:

 

870 = 2 * (2W - 75) + 2W

 

870 = 4W - 150 + 2W

 

Add 150 to both sides and combine terms:

 

1020 = 6W

 

Divide both sides by 6:

 

W = 170

 

The width of the base is 170 feet.

 

The length of the base is: 2W - 75, 2 * 170 -75, or 265 feet.

 

Questions?