Question 1180394: The perimeter of a triangle is 30 inches. The length of the shortest side is 1/3 the length of the hypotenuse, and 0.5 times the length of the remaining side. What is the length of the shortest side?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
The perimeter of a triangle is 30 inches. The length of the shortest side is 1/3 the length of the hypotenuse,
and 0.5 times the length of the remaining side. What is the length of the shortest side?
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Let x be the shortest side (the shortest leg) length.
Then the other leg is 2x, and the hypotenuse is 3x.
The Pythagoras equation is then
x^2 + (2x)^2 = (3x)^2, or
x^2 + 4x^2 = 9x^2, or
5x^2 = 9x^2, or
5 = 9,
which NEVER may happen.
The ANSWER and the DIAGNOSIS are:
such a triangle DOES NOR EXIST.
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Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The given information tells us that the lengths of the three sides are x, 2x, and 3x.
But three sides of lengths x, 2x, and 3x do not form a triangle, because the length of the longest side is only equal to the sum of the lengths of the other two sides.
Since the sum of the lengths of the two shorter sides is exactly equal to the length of the longest side, you have a degenerate triangle.
The perimeter of the triangle is supposed to be 30 inches. With side lengths x, 2x, and 3x, the lengths of the sides of the triangle are 5, 10, and 15 inches.
So you could say the triangle is a degenerate triangle with shortest side of length 5 inches.
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