SOLUTION: A yard has a perimeter of 184 feet. If six times the length of the yard equals seventeen times the width, what are the dimensions?

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Question 949275: A yard has a perimeter of 184 feet. If six times the length of the yard equals seventeen times the width, what are the dimensions?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
L=length=6/17W; W=width=17/6L; P=perimeter=2(L+W)
6L=17W Divide each side by 17
(6/17)L=W Multiply each side by 17/6
L=(17/6)W
P=2(L+W)
184 ft=2(L+W) Divide each side by 2.
92 ft=L+W Substitute for L.
92 ft=(17/6)W+W Combine like terms.
92 ft=(17/6)W+(6/6)W
92 ft=(23/6)W Multiply each side by (6/23)
(6/23)(92 ft)=W
6*4 ft=W
24 ft=W ANSWER 1: The width is 24 ft.
L=(17/6)W
L=(17/6)(24 ft)
L=17*4 ft=68 ft ANSWER 2: Length is 68 ft.
The yard is 68 feet by 24 feet.
CHECK:
Perimeter=2(L+W)
184 ft=2(68 ft + 24 ft)
184 ft=2(92 ft)
184 ft=184 ft