Posted by Liz on Sunday, September 7, 2008 at 3:57pm.
From the description above, we know that:
(W+2) x L = 140
(L+1) x W = 120
where W = the width and L is the length, so...
WL + 2L = 140
WL + W = 120
Subtract the second equation from the first, you get...
2L - W = 20, so
W = 2L - 20.
So feed that back into the first of the original two equations:
(2L - 18) x L = 140
2Lē - 18L - 140 = 0
so Lē - 9L - 70 = 0
factorize it: (L - 14)(L + 5) = 0
so L = 14 or L = -5. The latter is impossible, so L = 14.
But W = 2L - 20, so W = 8.
Check it:
(W+2) x L = 10 x 14 = 140 Correct.
(L+1) x W = 15 x 8 = 120 Correct.
Answer: W = 8; L = 14.
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