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The perimeter of a rectangular field is P feet. The width of the field is 200 feet less than its width. In terms of P, what is the length of the field in feet?

Please include the steps towards getting the answer. Thanks!

2007-07-12 18:08:07 · 11 answers · asked by Karina C. 2 in Science & Mathematics Mathematics

11 answers

The width of the field is 200 feet less than its width? I don't even know what that means, so I'm going to go ahead and assume you meant that the width is 200 feet less than the LENGTH.

l = length, w = width

P = 2l + 2w 2l = P - 2w

and we know that l = w + 200

Thus, P = 2(w + 200) + 2w

P=2w + 400 + 2w
P= 4w + 400
4w = P - 400
w = P/4 - 100

finally

l = w + 200 = P/4 + 100

I hope you understood that.

2007-07-12 18:24:55 · answer #1 · answered by wolfey6 2 · 0 0

Let P = the perimeter of the rectangle.
Let L = the length of the rectangle.
Let W = the width of the rectangle.
Since L will be 200 feet longer than the width,
Ergo, L = W + 200

Based on common knowledge, the perimeter of a rectangle is the total length of all four sides.

Since there are two equal widths and two equal lengths, the
perimeter formula is:

P = 2L + 2W

substituting our definition at the beginning that
L = W + 200,

then, P = 2(W+200) + 2W
P = 2w + 400 + 2 W
P = 4w + 400
w= (P- 400)/4

Now that we know the value of W in terms of P, we
can compute the value of L as required by your problem:

L = w + 200

substituting our W value into the equation,

L = (P -400)/4 + 200 THE ANSWER

This indeed is the "length" of the required solution to your problem. You have a great, blessed evening! (Hopefully,
in a bed with adequate "width").

2007-07-13 01:46:04 · answer #2 · answered by the lion and the bee 3 · 0 0

First, I think you meant that the width of the field is 200 ft less than its width.

a) let L = length of field
the W = width of field. Note that
W = L - 200.

b) Perimeter P = 2L + 2W (the length around the field)
= 2L + 2(L-200) or

P = 2L +2L -400, or
P = 4L - 400. So,

4L = P + 400 or
L = P/4 + 100

2007-07-13 01:16:46 · answer #3 · answered by pbb1001 5 · 1 0

The general formula is P = 2L + 2W Your info says that ... um. I see a typo. I will assume you meant "The width of the field is 200 feet less than its length." So you said that W=L-200. So by substitution, now P = 2L + 2(L-200) or P = 4L - 400. To get L alone you want to add 400 to both sides, then divide both sides by 4, thus... L = (P+400)/4

2007-07-13 01:16:04 · answer #4 · answered by LaWeezel 4 · 0 0

P = 2w + 2L

w = L - 200

P = 2(L - 200) + 2L

P = 2L - 400 + 2L

P = 4L - 400

P + 400 = 4L

P/4 + 400/4 = L

L = P/4 + 100

2007-07-13 01:17:37 · answer #5 · answered by Anonymous · 0 0

Let sides be x and x - 200
P = 2x + 2(x - 200)
P = 4x - 400
4x = P + 400
x = P/4 + 100
Sides are P/4 + 100 ft and P/4 - 100 ft

2007-07-13 03:52:45 · answer #6 · answered by Como 7 · 0 0

P=2W+2L
W=L-200 it's given,though, you stated it incorrectly.
P=2(L-200) + 2L
P= 2L-400+2L
P= 4L-400 add +400 to both sides of the equation
P+400=4L-400+400
P+400=4L divide both sides by 4
L=P+400/4

2007-07-13 01:51:35 · answer #7 · answered by Anonymous · 0 0

Width is 200 feet less than its length, therefore,
B=L-200

P=2(L+B)
P=2(L+L-200)
P=4L-400
L=(P+400)/4 feet

2007-07-13 01:15:32 · answer #8 · answered by Jain 4 · 0 0

w the width
l the length
p=2w+2l
p=2(l-200)+2l
p=4l-400
l=(p+400)/4
l=p/4+100

2007-07-13 01:20:33 · answer #9 · answered by zohair 2 · 0 0

you need 2 restate the ? and give more information

2007-07-13 01:16:33 · answer #10 · answered by RobertS 1 · 0 0

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