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.

Question

Amour

Mathematics

2 October, 10:52

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.

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Nola · 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