SOLUTION: I know how to set this up partially but I need help. A rectangle is 3 times as long as it is wide. If its length iand width are both decrased by 2cm , its area decreasd by 36 cm^2.

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Question 235188: I know how to set this up partially but I need help. A rectangle is 3 times as long as it is wide. If its length iand width are both decrased by 2cm , its area decreasd by 36 cm^2. find its orginal dimensions.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle is 3 times as long as it is wide.
Let x = the original width
then
3x = the original length
and
3x^2 = the area of the original rectangle
:
" If its length and width are both decreased by 2cm , its area decreased by 36 cm^2. find its original dimensions."
(x-2) = new width
(3x-2) = new length
and
(x-2)*(3x-2) = new area
FOIL
3x^2 - 2x - 6x + 4
3x^2 - 8x + 4 = the new area
:
Original area - new area = 36 sq/cm
3x^2 - (3x^2 - 8x + 4) = 36
Remove brackets
3x^2 - 3x^2 + 8x - 4 = 36
8x = 36 + 4
8x = 40
x = 5 cm is the original width
then
3(5) = 15 cm is original length
;
:
Check solution (new width = 3, new length = 13
15 * 5 = 75
13 * 3 = 39
-------------
diff = 36