Question

A rectangular Persian carpet has an area of (x^2+x-20) square feet and a length of (x+5) feet. The Persian carpet is displayed on a wall. The wall has a width of (x+2) feet and an area of (x^2+17x+30)square feet. Find the dimensions of the rug and the wall if x=20 feet.

Answer 1

Let x = 20 feet
area of carpet rug = x^2 + x -20
area of carpet rug = (20ft)^2 + (20) -20 = 20^2 = 400 ft. squared
length of carpet rug = x + 5 = 20 + 5 = 25 feet.
but area of carpet rug = l x b which is 400 ft.squared
that is area of carpet rug = (25feet) x b = 400 ft squared
b = 400ft.sq /25 ft = 16ft
so, dimensions of rug = 25ft x 16ft = 400ft squared

wall width = x+ 2 feet = 20 + 2 feet = 22 feet
area of wall = x^2 + 17x +30 sq.ft
area of wall = (20)^2 + 17(20) + 30 sq.ft
area of wall = 400 +340 + 30 sq.ft
area of wall = 770 sq.ft
so, if wall dimensions = length x width = 770 sq.ft
and wall width = 22 feet length
then wall width = 770 sq.ft/22 feet = 35 feet