What would be my equations to set up this problem?

Question

The area of a rectangle is 15 square feet. If the width is 2 feet less than its length find the dimensions.

Answer 1

Let x = length of rectangle (in feet)

Let x-2 = width of rectangle (in feet

 

To find the area of the rectangle, we multiply length times width; setting this equal to 15

 

(x) * (x-2) = 15

 

Which gives us:

 

x² - 2x = 15

 

Subtract 15 from both sides to give us:

 

x² - 2x - 15 = 0

 

Next, factor this out to be:

 

(x + 3) (x - 5) = 0

 

x + 3 = 0; subtract 3 from both sides, gives x= -3 (not a valid length)

 

x - 5 = 0; add 5 to both sides, which gives x=5

 

To text this:  Length of 5

                    Width of 5-2 = 3

 

Multiply length x width:  5 * 3 = 15   [Check]