Problema Solution
T wants to buy a rug that is 9 feet wide and 18 feet long. She wasnts to leave a uniform strip of floor around the rug.She can afford to buy 112 square feet of carpet. What dimensions should the rug have?
Answer provided by our tutors
carpet area = 112 ft^2
let width be x of the strip
width of rug = 9-2x
length of rug = 18-2x
So, (9-2x)(18-2x)=112
162-36x-18x+4x^2=112
4x^2-54x+50=0
4x^2-4x-50x+50=0
4x(x-1)-50(x-1)=0
(x-1)(4x-50)=0
x=1, 12.50
So, the width of uniform strip=1.
Width of rug=9-2x=9-2=7 feet
Length of rug=18-2x=18-2=16 feet