Base Width and Length

Question

A building in a city has a rectangular base. The length of the base measures 75ft less than twice the width.The perimeter of the base is 750ft. What are the dimensions of the base.

Answer 1

Hello Marjorie,

Let W = the width of the rectangle and

let L = the length.

 

From the second second sentence, we have that

L = 2W - 75 {Equation 1}

 

The formula to find the perimeter of a rectangle is:

P = 2W + 2L {Equation 2}

 

We are told the perimeter is 750.  Using that, and plugging {Equation 1} into {Equation 2}, we get

750 = 2W + 2(2W - 75)

→ 750 = 2W + 4W -150

→ 750 = 6W - 150

→ 6W = 900

→ W = 150.

 

Then using {Equation 1},

L = 2(150) - 75

→ 300 - 75

→ 225

 

So the dimensions are 150 by 225.

 

Hope the above helps, and thank you for posting the question.

 

Kind regards,

Michael E.

Answer 2

Good morning Marjorie,

 

The perimeter of the base is equal to L + L + W+ W=(2L+ 2 W)

 

We don't know either L or W but L = 2W - 75 according to the problem (75 less than twice the width)

 

So we substitute (2W - 75) in for L and add up what we have using the equation in bold

 

2 (2W - 75) + 2W 

 

We set this equal to the perimeter which is 750 

 

2 (2W - 75) + 2W =750

 

Distribute the 2

 

4W - 150 + 2W = 750

 

6W - 150 = 750

 

6W = 900

 

W = 150

 

The length is 75 less than twice this.

 

L = 2 (150) - 75 = 225

 

So the width is 150 ft and the length is 225 ft.

 

And to check the work, 150 + 150 + 225 + 225 = 750

 

I hope this helps