SOLUTION: My daughter and I are arguing over this problem. So a second opinion would be greatly appreciated. A rectangle has a length that is 4 feet greater than its width. If each side

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Question 972887: My daughter and I are arguing over this problem. So a second opinion would be greatly appreciated.
A rectangle has a length that is 4 feet greater than its width. If each side of the rectangle is increased by 3 feet, write an equation to represent the area of the new rectangle. My daughter's answer was
4x^2+15x+9.
Please show steps. I incorrectly submitted wrong numbers before, so having difficulty explaining.
Thanks in advance and any feedback is appreciated.
Found 2 solutions by macston, MathTherapy:
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
.
W=original width; L=original length=W+4ft
W+3ft=new width; L+3ft=new length=W+7ft
.
NewArea=new length x new width

.
ANSWER: This is the equation:Area=
.
CHECK: (The assigned width is arbitrary, just to check. Any number will work.)
Let W=2 feet
L=W+4ft=6 feet
New length=L+3 feet=6 feet+3 feet=9 feet
New width=W+3 feet=2 feet+3 feet=5 feet
New Area=new length x new width=9 feet x 5 feet=45 square feet
.
CHECK New Equation:



Same as using (new length) x (new width)
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

My daughter and I are arguing over this problem. So a second opinion would be greatly appreciated.
A rectangle has a length that is 4 feet greater than its width. If each side of the rectangle is increased by 3 feet, write an equation to represent the area of the new rectangle. My daughter's answer was
4x^2+15x+9.
Please show steps. I incorrectly submitted wrong numbers before, so having difficulty explaining.
Thanks in advance and any feedback is appreciated.
Let rectangle's width be W

Then its length = W + 4

An increase of 3 feet makes the new width: W + 3

An increase of 3 feet makes the new length: W + 4 + 3, or W + 7

New area = new width, times new length, OR (W + 3)(W + 7)

This expands, by distribution, to: Area =  

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