Math
posted by Liz on .
If the width of a rectangle is increased by 2 inches, the area is 140 square inches. If the legnth is increased by 1 inch, the area is 120 inches. Find the dimensions of the rectangle.

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
2L²  18L  140 = 0
so L²  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.