SOLUTION: Use an Algebraic equation to determine each rectangle's dimensions. An American football field is a rectangle with a perimeter of 1040 feet. The length is 200 feet more than the

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Question 1153483: Use an Algebraic equation to determine each rectangle's dimensions.
An American football field is a rectangle with a perimeter of 1040 feet. The length is 200 feet more than the width. Find the width and length of the rectangular field.
Thank you in advance,
SYL
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


w = width; w+200 = length

perimeter = 2(length+width)

2%28w%2B%28w%2B200%29%29+=+1040

Solve using basic algebra....

Without algebra....

Imagine shortening the field by 200 feet, so that the length and width are the same. That makes the perimeter 1040-400 = 640 feet.

With length and width the same, the field is square; each side is one-quarter of the perimeter: 640/4 = 160.

So the width of the field is 160 feet.

Now add the 200 feet back on to the length to get 360 feet for the length.

ANSWER: width 160 feet; length 360 feet

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

An American football field is a rectangle with a perimeter of 1040ft.
the perimeter of a rectangle is:
P=2%28L%2BW%29....if P=1040ft
2%28L%2BW%29=1040ft
L%2BW=1040ft%2F2
L%2BW=520ft........eq.1

if the length is 200ft+more than the width, we have
L=W%2B200ft........eq.2
go to
L%2BW=520ft........eq.1, substitute L
W%2B200ft%2BW=520ft........solve for W
2W=520ft-200ft
2W=320ft
W=320ft%2F2
W=160ft

go to
L=W%2B200ft........, substitute W
L=160ft%2B200ft
L=360ft

answer: the width is 160ft and length of the rectangular field is 360ft