SOLUTION: The length of a rectangle exceeds its width by 6 units. If each dimension were increased by 3 units ,the area would be increased by 57 square miles. Find the dimensions of the orig

Algebra ->  Rectangles -> SOLUTION: The length of a rectangle exceeds its width by 6 units. If each dimension were increased by 3 units ,the area would be increased by 57 square miles. Find the dimensions of the orig      Log On


   

Question 1088545: The length of a rectangle exceeds its width by 6 units. If each dimension were increased by 3 units ,the area would be increased by 57 square miles. Find the dimensions of the original rectangle ive been trying and i cant solve this
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle exceeds its width by 6 units.
If each dimension were increased by 3 units ,the area would be increased by 57 square miles.
Find the dimensions of the original rectangle
:
L = (w+6)
L*W = the area of the original rectangle
and
(L+3)*(w+3) = the increased area
Foil
Lw + 3L + 3w + 9 = new area
:
New area - original area = 57 sq/units
Lw + 3L + 3w + 9 - Lw = 57
lw - Lw + 3L + 3w + 9 = 57
3L + 3w = 57 - 8
3L + 3w = 48
simplify, divide by 3
L + w = 16
replace L with (w+6)
w + 6 + w = 16
2w = 16 - 6
2w = 10
w = 5 units is the width of the original rectangle
then
5 + 6 = 11 units is the length
:
:
Check this, new rectangle is 14 by 8
14*8 - 11*5 =
112 - 55 = 57