Question 83471
Let the length be x ft and the width be y ft.
The perimeter is 88ft

==>  2(l + w) = 88

==> l + w = 88/2

==>  l + w = 44 

==> w = 44 - l  -------------------(1)

Given area = 480

==>  l x w = 480

==> l (44-l) = 480

==> 44l - l^2 = 480

==> - l^2 + 44l - 480 = 0

==> l^2 - 44l + 480 = 0

==> l^2 - 20l - 24l + 480 = 0

==> l(l-20) - 24(l - 20) = 0

==> (l - 20) ( l- 24) = 0

==> l-20 = 0  or l - 24 = 0

==> l = 20 or l = 24

==> w = 24 0r w = 20

Thus the dimensions of the retangular room are 20 ft and 24 ft.