What is the width of the retangle?

Question

The width of a retangle is 2 feet shorter than its length. If its width is decreased by 1 foot and its length is increased by 4 feet, its area would be increased by 21 square feet. what is the width of the retangle?

Answer 1

Hi Cindy, let w represent the width of the rectangle and l represent the length of the rectangle.

 

Given, the width, w, is equal to l - 2.

 

The area of the original rectangle would be, area = l * w, or area = l * (l -2), which gives the original area as l² - 2l.

 

The width is reduced by 1 foot and the length is increased by 4 feet. The new area is given by, area = (l + 4) * (l - 1), or    

l² + 3l - 4.

 

The new area is equal to the original area plus 21 square feet.

 

Equation to solve:

 

New area = original area + 21

 

l² + 3l - 4 = l² - 2l + 21

 

The l² terms cancel leaving:

 

3l - 4 = 2l + 21

 

Combine terms:

 

5l = 25

 

l = 5

 

The original length was 5 feet.

 

The original width was 5 - 2, or 3 feet.

 

The new length is 5 + 4, or 9 feet.

 

The new width is 5 - 1, or 4 feet.

 

The original area is 3 * 5, or 15 square feet.

 

The new area is 4 * 9, or 36 square feet.

 

The difference in areas, 36 - 15 = 21 square feet.

 

Questions?