quadradics problem

Question

if a rectangular carpet has a perimeter of 120 feet and an area of 800 square feet, what is it width?

Answer 1

Perimeter = 2(length + width)

 

2(L+w) = 120

L + w = 60

 

Lw = 800

 

From 1st equation w = 60-L

 

L(60-L) = 800

60L - L² - 800 = 0

Multiply through by -1 and put in descending order of exponents:

L² - 60L + 800 = 0

 

(L-40)(L-20) = 0

L = 40 or L = 20

 

The dimensions are 40 ft by 20 ft