<PRE><B>Question 1145450</B>
area = 18 = l * w
perimeter = 18 = 2l + 2w
l = length
w = width


since both equal 18, then l * w = 2l + 2w
in l * w = 18, solve for l to get l = 18/w


in 2l +2w = 18, replace l with 18/w to get:
2 * (18/w) + 2w = 18
simplify to get:
36/w + 2w = 18
multiply both sides by w to get:
36 + + 2w^2 = 18w
subtract 18w from both sides to and order by descending order of degree to get:
2w^2 - 18w + 36 = 0
divide both sides by 2 to get:
w^2 - 9w + 18 = 0
factor to get:
(w-3) * (w-6) = 0
solve for w to get:
w = 3 or w = 6.


if w = 3, then l = 6 and you get:
l * w = 6 * 3 = 18
2l + 2w = 2*6 + 2*3 = 12 + 6 = 18


if w = 6, then l = 3 and you get:
l * w = 3 * 6 = 18
2l + 2w = 2*3 + 2*6 = 6 + 12 = 18


the dimensions of the dining room are 3 by 6 or 6 by 3, however you want to show it.
usually the length is the longer side, so length = 6 and width = 3 sounds like a good way to present it.


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