Factoring for Algebra

Question

solve by factoring: Ms. K and Ms. B want to build an alpaca farm. A plot of land for sale has a width of x yards and a length that is 8yds less than its width. Ms. B and Ms. K will only purchase the land it if measures 240 square yards. What value of x will cause them to purchase the land?

Answer 1

Let x=width

Let x-8=length

Formula: Area = length x width

Plugging values in:

240 = x(x-8) Distribute

240 = x²-8x Subtract 240 from both sides

0=x²-8x-240 Factor

0=(x-20)(x+8) Set factors = 0 and solve

x-20=0 Add 20 to both sides

x=20

x+8=0 Subtract 8 from both sides

x=-8 (This cannot be a valid solution, width cannot be negative)

length = x-8 = 20-8 = 12

The dimensions would be 20 yd x 12 yd