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Question 51327This question is from textbook college algebra
: Please help...got stuck on this problem for long time...thank you!!
"Fencing Dog Pens" Clint is constructing 2 adjacent rectangular dog pens. Each pen will be three times as it is wide, and the pens will share a common long side. If Clint has 65ft of fencing, what are the dimensions of each pen??
This question is from textbook college algebra
Found 2 solutions by rapaljer, Earlsdon:
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let x = width of each pen, assuming that the there will be two pens adjacent to each other, sharing a common length, which is to be 3x.
If you draw the picture, you will have three lengths (since there is a shared length), each of which is 3x in length. There will be a total of 4 widths for the two pens, each of which is x.
Total fence required would be
3(3x) + 4(x) = 65 feet
9x + 4x = 65
13x = 65
x= 5 feet width.
3x= 15 feet length.
The pens are 5 ft by 15 feet.
R^2 at SCC
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! I assume that you meant to write..."Each pen will be three times as long as it is wide,..."
If we let the width be W, then the length of each pen will be: L = 3W.
From the problem description, the two adjacent pens will have three long sides and four short sides.
Each long side will be 3W in length and there are three of these,
so we have 3(3W) = 9W. This is the total of the lengths.
The short sides (Widths) wll each be W in length and there are four of these, so we have 4(W) = 4W This the total of the widths.
Adding up all of these, we get:
9W + 4W = 13W and this is equal to the total length of the fence (perimeter) of 65 feet.
13W = 65 Divide both sides by 13.
W = 5 feet.
This is the length of each width, but there are four of these, so we have the total for the widths is: 4(5) = 20 feet.
The length, L = 3W = 3(5) = 15 feet
The three lengths is then: 3(15) = 45 feet.
Each pen measures: (L X W) = 15 ft. by 5 ft.
Check:
Adding up the the total widths and the total lengths, we get: 20 ft + 45 ft = 65 ft.
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