Question

Find the dimensions of a rectangular Persian rug whose perimeter is 18 ft and whose area is 20ft^2. *Answer fill in*The Persian rug has a length (longerside) of [___]ft and a width (shorter) of [__]ft

Answer 1

Perimeter = 18 ft

Area = 20 ft ^2

Perimeter = 2l + 2w

Area = lw

Substitution

18 = 2l + 2w

20 = lw

Solve for l

20/w = l

18 = 2(20/w) + 2w

18 = 40/w + 2w

18w = 40 + 2w^2

2w^2 - 18w + 40 = 0

w^2 - 9w + 20 = 0

(w - 5)(w - 4) = 0

w1 = 5 w2 = 4

Conclusion

width = 4 ft

length = 5 ft