Question 173857
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 squared(or raise to the
 2nd power.) Find its original dimensions.
:
Original rectangle:
Let x = the width
then
3x = the length
and
Area = 3x^2
:
"if its length and width are both decreased by 2cm, its area is decreased by 36 sq/cm"
(3x-2)*(x-2) = 3x^2 - 36
FOIL
3x^2 - 6x - 2x + 4 = 3x^2 - 36
3x^2 - 8x + 4 = 3x^2 - 36
3x^2 - 3x^2 - 8x = - 36 - 4
-8x = -40
x = {{{(-40)/(-8)}}}
x = +5 cm is the original length
then
3*5 = 15 cm is the original length
;
:
Check solution in the statement:
"its length and width are both decreased by 2cm, its area is decreased by 36cm"
13 * 3 = (15*5) - 36
39 = 75 - 36