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Can someone with math smarts help me out?
Clint is constructing 2 adjacent rectangular dog pens. Each pen will be three times as long as it is wide, and the pens will share a common long side. If Clint has 65 ft. of fencing, what are the dimensions of each pen? I can't figure out how to do this one, so I need an example to compute this problem. THANX IN ADVANCE!! GOD BLESS!!! |
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Diamond Enthusiast![]() |
word problems are just a matter of converting English to Math. Mathlish?
If we define the Width of 1 of the pens =W The statement says the lenghth is 3 times as long so 3W = length We count up the sides of pens W + 3W +W + 3W equals 1 pen We share 1 fence with both pens so the 2nd pen is W+3W + W The perimeter is the sum of all the lengths 13W's We know that we have 65Ft 65ft = 13 W's solve for W check your answer |
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Diamond Enthusiast ![]() |
So that you can have a chance to try this yourself, I'll change a few numbers. Lets say that the long side of the rectangles has to be twice as, long as the short side and that Chris has 100 feet of fence.
Lets use letters to represent the lenghts. We'll say L is the length of the long side and S is the length of the short side. Each rectangle has 2 short sides and 2 long sides, but 1 of the long sides is used by both rectangles so we really have 3 long sides (1 from each of the two rectangles and 1 shared) and 4 short sides (2 from each of the two rectangles). In terms of total lenght, then, we have: 3 x L + 4 x S We know from the question that the total length of fence it 100, so we know 3 x L + 4 x S = 100 We also know from the question that each long side is twice as long as each short side, so 2 x S = L We can combine the last two equations by putting 2 x S everywhere we see L in the earlier equation. This gives us: 3 x 2 x S + 4 x S = 100 Simplifying a little be solving 2 x 3, we find 6 x S + 4 x S = 100 I've forgotten the name for this rule, but we can rearrange to get (6 + 4) x S = 100 Then simplifiy: 10 x S = 100 Then divide both sides by 10: 10 x S ÷ 10 = 100 ÷ 10 Simplifying: S = 10 Recalling that we know that 2 x S = L we can solve for L by putting the value we now know in place of S 2 x 10 = L So L = 20 |
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