SOLUTION: A rectangle is three times as long as it is wide. If its lenght and width are both decreased by 2cm, its area is decreased by 36cm^2. Find its original dimensions. Make a sketch

Question 174033: A rectangle is three times as long as it is wide. If its lenght and width are both decreased by 2cm, its area is decreased by 36cm^2. Find its original dimensions. Make a sketch
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangle is three times as long as it is wide. If its length and width
are both decreased by 2cm, its area is decreased by 36cm^2.
Find its original dimensions. Make a sketch
:
Let x = the width
then
3x = the length
and
3x^2 = original area
:
(x-2) = new width
(3x-2) = new length
and
(x-2)*(3x-2) = new area
FOIL
(3x^2 - 8x + 4) = new area
:
Original area - new area = 36 sq/cm
3x^2 - (3x^2 - 8x + 4) = 36
3x^2 - 3x^2 + 8x - 4 = 36
8x = 36 + 4
x =
x = 5 cm; original width
then
3(5) = 15 cm; original length
:
:
Check solution (new rectangle: 13 by 3)find the areas
75 - 39 = 36
:
I'll let you do the sketching
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