SOLUTION: The length of a rectangle is twice as long as the width. If one centimeter is taken off of each edge the area equals 1 meter. Find the dimensions of the rectangle.

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle is twice as long as the width. If one centimeter is taken off of each edge the area equals 1 meter. Find the dimensions of the rectangle.       Log On


   

Question 1065314: The length of a rectangle is twice as long as the width. If one centimeter is taken off of each edge the area equals 1 meter. Find the dimensions of the rectangle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you mean the area is 1 square meter since meter is a measure of length not area.
.
.
100 cm=1 meter
and
L=2W
and for a rectangle,
A=LW
Convert from square meters to square centimeters to use consistent units,
%28L-1%29%28W-1%29=%28100%29%28100%29
%28L-1%29%28W-1%29=1000
So then substituting from above,
%282W-1%29%28W-1%29=1000
2W%5E2-2W=W%2B1=1000
2W%5E2-3W-999=0
Complete the square,
2%28W%5E2-%283%2F2%29W%2B%283%2F4%29%5E2%29=999%2B2%283%2F4%29%5E2
2%28W-3%2F4%29%5E2=7992%2F8%2B9%2F8
2%28W-3%2F4%29%5E2=8001%2F8
%28W-3%2F4%29%5E2=8001%2F16
W-3%2F4=0+%2B-+sqrt%288001%29%2F4
W=3%2F4+%2B-+%283%2F4%29sqrt%28889%29
W=%283%2F4%29%281%2B-sqrt%28889%29%29
Only the positive value makes sense in this problem,
W=%283%2F4%29%281%2Bsqrt%28889%29%29cm
and
L=2%283%2F4%29%281%2Bsqrt%28889%29%29
L=%283%2F2%29%281%2Bsqrt%28889%29%29cm