SOLUTION: Emma wants to start with a square patio and experiment with the sides to see how changing the length of the sides affects the area and shape of the patio. She doesn't care if the n

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Question 163393: Emma wants to start with a square patio and experiment with the sides to see how changing the length of the sides affects the area and shape of the patio. She doesn't care if the new patio is no longer a square but still wants it to be rectangular. The patio is attached to the house. If emma starts with calling the length of the side patio x, what is the perimeter? What are the dimensions? What is the area?
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
L = length
W = width
assume the length will be against the house.
length can be less than width if need be.
length can be same as width if need be (square).
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formula for Area of patio is length * width = L*W.
formula for perimeter of patio is L + 2W.
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this is because you do not want to include the length of the patio that is against the house in determining material required for the perimeter.
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if she calls the length "x", then the width can be anything in terms of x.
L = x
W = 2*x
W = x+c where c is a constant.
W = x-c where c is a constant.
W = x/2
any of these will work.
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in the area formula, you substitute x for L and substitute whatever the value you want for W in terms of x.
example:
L = x
W = 2*x+3
then A (area) = L*W = x*(2*x+3)
P = L + 2*W = x + 2*(2*x+3)
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just give x a value and everything else falls into place.
example:
let x = 15
L = x
W = 2*x+3
substituting 15 for x gets
L = 15
W = 33
A = L*W = 15*33
P = L + 2*W = 15 + 2*33
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