SOLUTION: The length of a rectangle is 7 feet longer than it is wide. If each side is increased 7 feet, then the area is multiplied by 4. What was the size of the original rectangle?
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Question 855192: The length of a rectangle is 7 feet longer than it is wide. If each side is increased 7 feet, then the area is multiplied by 4. What was the size of the original rectangle? Answer by dkppathak(439) (Show Source):
You can put this solution on YOUR website! The length of a rectangle is 7 feet longer than it is wide. If each side is increased 7 feet, then the area is multiplied by 4. What was the size of the original rectangle?
Answer
Let width of rectangle is x feet
length will be x+7 feet
area of rectangle =lenghxwidth
area of rectangle =x(x+7)
now as per given conditions if 7 feet is increased area willbe 4 times
new width =x+7
length =x+7+7=x+14
new area will be =(x+7)(x+14)
as per given conditions
(x+7)(x+14)=4x(x+7)
x^2+21x+98=4x^2+28x
0=4x^2+28x-x^2-21x-98
3X^2+7x-98=0
3x^2-14x+21x-98=0
x(3x-14)+7(3x-14)=0
x+7=0 or 3x-14=0
x=-7 0r x=14/3 feet
neglecting negative 7 as diamension can not be negative
width =14/3 feet
and length=14/3+7=35/3 feet
Answer
length will be =35/3 feet
width will be =14/3 feet
verification
area=14/3x35/3
new area will be
=56/3x35/3=4(14/3x35/3) verified as per condition area 4 times of old area
