SOLUTION: A rectangle corner lot has a width 12 feet less than its length. When three feet are taken from one width and one length, to be used as a sidewalk, the area of the lots is reduced

Algebra ->  Rectangles -> SOLUTION: A rectangle corner lot has a width 12 feet less than its length. When three feet are taken from one width and one length, to be used as a sidewalk, the area of the lots is reduced       Log On


   

Question 1002518: A rectangle corner lot has a width 12 feet less than its length. When three feet are taken from one width and one length, to be used as a sidewalk, the area of the lots is reduced by 177ft(2). Find the original dimensions of the lot.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This sidewalk is only going half-way around, and will not be a perimeter border.

L for lot length
w for lot width
-
w=L-12
Total Lot, w%2AL square feet
Reduced Lot, %28w-3%29%28L-3%29
Sidewalk area is the total lot area minus the reduced lot area.
wL-%28w-3%29%28L-3%29=177---first, simplify this.

wL-%28wL-3L-3w%2B9%29=177
wL-wL%2B3L%2B3w-9=177
3L%2B3w-9-177=0
3L%2B3w-186=0
Substitute for w, from the description fact.
3L%2B3%28L-12%29-186=0
3L%2B3L-36-186=0
6L=186%2B36
6L=222
highlight%28L=37%29 and from this find that highlight%28w=25%29.