SOLUTION: What are the dimensions of a rectangle whose perimeter is 48 meters and whose area is 135 square meters?

Question 269821: What are the dimensions of a rectangle whose perimeter is 48 meters and whose area is 135 square meters?
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
(i) P = 2L + 2W
we know that P = 48, so we get
(ii) 48 = 2L + 2W
dividing by 2 we get
(iii) 24 = L + W
solving for L, we get
(iv) L = 24 - W
--------
(v) A = LW
We know that A = 135, so we get
(vi) 135 = LW
substituting (iv) into (vi) we get
(vii) 135 = (24-W)(W)
expanding we get
(viii) 135 = -W^2 + 24W
setting = 0 we get
(ix) W^2 - 24W + 135 = 0
factoring, we get
(x) (W-15)(W-9) = 0
and then
W = 15
or
W = 9
----
answer: W = 9, L = 15 ; W = 15, L = 9
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