Question 503953: The length of a rectangular garden is 8 feet longer than its width. If the garden's perimeter is 184 feet, what is the area of the garden in square feet?
Found 2 solutions by oberobic, nic0le116:
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! L = length
W = width
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L = W+8
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P = perimeter
P = 2(L+W)
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P =184 (given)
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substitute L=W+8 in the perimeter equation
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2( (W+8) + W ) = 184
(W+8) +W = 92
2W + 8 = 92
2W = 84
W = 42 ft
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L = W+8
L = 42+8
L = 50 ft
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Always check your work.
In this case check the perimeter.
2(L+W) = ?
2(50+42) = 184
Correct.
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Re-read the question to make sure you answer it.
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Oh, it asks for the area in square feet.
OK.
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A = area
A = L*W
A = 50 ft * 42 ft
A = 2100 sq ft
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Done.
Answer by nic0le116(25) (Show Source):
You can put this solution on YOUR website! I always recommend drawing a picture for problems like these.
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What can we use to represent the value of the width right now?
Since we can not answer with a numerical value at this time, it is "x."
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What can we use to represent the value of the length at this time?
Since all we now is that it is 8 ft longer then the width, we can represent it as "x+8"
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Since we also know the value of the perimeter...how can we solve to find the value x to solve for length and width?
Since we know Perimeter is the value of all the sides added up, we can conclude in the case of a rectangle that the value is 2 times the width +2 times the length.
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Now, set up a problem to determine x using all the information we currently have.
What did we use for width- x
and length?- x+8
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Now lets use that 2 times length + 2times width= perimeter to figure out what x is!
2x+ 2(x+8)= 184 (distribute the 2)
2x+2x+16=184 (combine like terms)
4x+16=184 (subtract 16 from both sides)
4x=168 (divide by 4)
x=42
Now what does this x represent? The value of the width!
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Now how do we know what the length is?
Plug the value of x (42) into what we originally represented the length by which was(x+8)
42+8= 50
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Not sure if this is right? add it all up to see if it equals the perimeter.
42+42+50+50=184. CHECK!
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Now remember with word problems, sometimes you have to do some extra work. Always make sure you answered what was originally asked.
So we're not done yet!
We want to know the area, and now that we know the value of the length and width, we can do that.
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Area= L*W
42*50=2100
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