SOLUTION: one side of a triangle is 1 in. longer than the shortest side and is 1 in. shorter than the longest side. the perimeter is 17 in. what is dimensions of triangle?

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Question 94008This question is from textbook
: one side of a triangle is 1 in. longer than the shortest side and is 1 in. shorter than the longest side. the perimeter is 17 in. what is dimensions of triangle?
This question is from textbook

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Call the one side x inches
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Then another side is 1 inch smaller so it is x - 1 inches.
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And a third side is 1 inch longer so it is x + 1 inches.
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The perimeter is the sums of the lengths of the three sides. So we can add up the three sides
to get:
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x+%2B+x+-+1+%2B+x+%2B+1
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Note that the -1 and the +1 cancel each other. So what you are left with is:
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x+%2B+x+%2B+x+=+3x
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as being the sum of the three sides. But the sum of the three sides is 17 inches according to
the problem.
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Therefore, we have:
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3x+=+17
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You can then solve for x by dividing both sides by 3 to get:
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x+=+17%2F3
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On side is 1 inch smaller than that, but 1 inch is the same as 3%2F3 inches. So we can
subtract 3%2F3 inches from 17%2F3 inches to find that this second side has a
length of 17%2F3+-+3%2F3+=+%2817-3%29%2F3+=+14%2F3 inches.
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And the third side is 1 inch or 3%2F3 inches longer than x. So the third side is
given by:
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17%2F3+%2B+3%2F3+=+%2817%2B3%29%2F3+=+20%2F3 inches.
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And that's the answer. The three sides are 14%2F3, 17%2F3, and 20%2F3.
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You can check this answer by adding the three sides over their common denominator of 3
to get:
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+%2814%2B17%2B20%29%2F3+=+51%2F3+=+17 inches
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So our answer checks.
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Hope this helps you to understand the problem.
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