Translate to a quadratic? equation, quadratic formula.

Question

The length of a rectangular air filter is 5 inches less than twice the width. Find the length and width of the filter if the area is 273 square inches.

Answer 1

If we let the width = x, then the length = 2x - 5

 

Area = length x width

 

273 = x(2x - 5)

 

273 = 2x² - 5x

 

2x² - 5x - 273 = 0

 

(x - 13)(2x + 21) = 0

 

We can eliminate the second factor because dimensions cannot be negative.

 

So we let x - 13 = 0

 

x = 13 in. = the width

 

The length = 2x - 5 = 2 * 13 - 5 = 26 - 5 = 21 in.