Question 1145450: The perimeter of a rectangular dining room is 18 meters. The area is 18 square meters. What are the dimensions of the dining room? Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source):
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.
You can put this solution on YOUR website! The perimeter of a rectangular dining room is 18 meters. The area is 18 square meters. What are the dimensions of the dining room?
Let length and width be L and W, respectively
Then we get: 2(L + W) = 18_______2(L + W) = 2(9)______L + W = 9______L = 9 - W ---- eq (i)
Also, LW = 18 ------ eq (ii)
W(9 - W) = 18 ------ Substituting 9 - W for L
0 = (W - 6)(W - 3)
W - 6 = 0 OR W - 3 = 0
W, or width = 6 OR W = 3
If width = 6, then length = 3(9 - 6), and VICE-VERSA.
