SOLUTION: i have a math problem that says to build (draw)a rectangular platform with a perimeter of 74 feet and an area of 340 square feet. how would I make this on paper

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Question 970238: i have a math problem that says to build (draw)a rectangular platform with a perimeter of 74 feet and an area of 340 square feet. how would I make this on paper
Found 2 solutions by macston, LinnW:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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L=length; W=width; P=perimeter; A=area
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P=2(L+W)
74ft=2(L+W)
37ft=L+W
37ft-W=L Use this to substitute for L.
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A=LW Substitute for L from above.
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340ft%5E2=%2837ft-W%29W
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340ft%5E2=37Wft-W%5E2 Add W%5E2-37Wft to each side
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W%5E2-37Wft%2B340ft%5E2=0
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%28W-20ft%29%28W-17ft%29=0
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W-20ft=0 or W-17ft=0
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W=20ft or W=17ft
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The width will be either 17 feet or 20 feet and the length will be the other.
For instance, with a width of 17 feet, the length would be 20 feet.
With a scale of 48:1 (4 feet=1 inch), you would draw a rectangle 5 inches long by 4 1/4 inches wide.


Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
The first step is the find the length and width of the platform.
The formula for perimeter is P = 2L + 2W
The formula for area is A = L * W
Since perimeter is 74, we have 74 = 2L + 2W
Since are is 340, we have 340 = L * W
For one of the two equations above we can solve for W in terms of L
Lets use 74 = 2L + 2W
add -2L to eac side
74 - 2L = 2W
dive each side by 2
(74-2L)/2 = 2W/2
37-L = W
Now substitute ( 37-L) for W in 340 = L * W
340 = L * ( 37-L)
340 = 37L - L^2
add -340 to each side
0 = -L^2 +37L -340
multiply each side by -1
L^2 -37L + 340 = 0
(L-17)(L-20) = 0
So L = 17 or L = 20
Since L is usually the longer dimension lets use L = 20
Since L*W = 340 we have 20*W = 340 so W = 17
The dimensions of our rectangle are 20 feet by 17 feet
The last part will be to draw this to scale.
If you use a scale of 1/2 inch = 1 foot, we wouls
want to draw a rectangle of 10 inches by 8.5 inches