Question 875359: A square with an area of 144 square centimeters was increased in length, but not width, until the resulting rectangle had a perimeter that was 4 times the perimeter of the original square. By how many square centimeters did the area of the figure increase?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A square with an area of 144 square centimeters was increased in length, but not width, until the resulting rectangle had a perimeter that was 4 times the perimeter of the original square.
By how many square centimeters did the area of the figure increase?
:
Let a = increase in length
The square root of 144 is 12 cm, the original side of the square
then
(a+12) = the increased length
:
4(12) = 48 cm is the original perimeter
;
The equation for the new perimeter
2(12) + 2(a+12) = 4(48)
24 + 2a + 24 = 192
2a = 192 - 48
2a = 144
a = 144/2
a = 72 is the amt added to the length
therefore
72+12 = 84 is the new length
and
84*12 = 1008 sq/cm is the area
1004 - 144 = 864 sq/cm increase in area when the perimeter is increased 4 times
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