The length of a rectangle is 6 more than the width. The area is 520 square yards. Find the length and width of the rectangle.

Question

Prep For College Math, module 7.11

Answer 1

The area of a rectangle is length times width.

 

Let width = x

Let length = x + 6

 

Using these variables, we can write an equation that represents the area.

 

x(x + 6) = 520

 

x² + 6x = 520

 

 

Subtract 520 on both sides of the equation.

 

x² + 6x - 520 = 0

 

 

We try to factor the left side using FOIL.

 

(x - 20)(x + 26) = 0

 

 

Set the factors equal to zero.

 

x - 20 = 0                and                 x + 26 = 0

 

x = 20                     and                 x = -26

 

Since we cannot have a negative value for a dimension, we accept the positive value x:

 

x = 20

 

This is your width.  Add this value of x to 6 to get your length.