Write an equation of the area of a rectangle with a missing side.

Question

The length of a rectangle is 9 less than twice its width and the area is 180. Write an equation and define the length and width.

Answer 1

The area of any rectangle is length times width.

 

Let width = x

Let length = 2x - 9

Area = 180

 

 

x(2x - 9) = 180

 

2x² - 9x = 180

 

 

Subtract 180 on both sides of equation.

 

2x² - 9x - 180 = 0

 

 

Use the quadratic formula to solve for x.

 

x = (9 ± √(81 - 4(-360))) / 4

 

x = (9 ± √(1521)) / 4

 

x = (9 ± 39) / 4

 

x = (9 + 39) / 4                and                   x = (9 - 39) / 4

 

x = 12                             and                    x = -7.5

 

 

Since we cannot have negative values for dimensions, we accept the positive value of x.

 

x = 12

 

 

Substitute this value of x into the dimensions to get your length and width.