Question 271066
x = longest side of triangle
y = 1/2x  :: y is half the longest side
z = x - 10  :: z is 10 less than the longest side
x + y + z = 53
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substituting
x + 1/2x + x-10 = 53
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multiply everything by 2
2x + x +2x -20 = 106
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collect and simplify
5x = 126
x = 126/5 = 25.2
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y = 1/2x = 25.2/2 = 12.6
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z = x-10 = 15.2
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checking,  does x+y+z = 53?
25.2 + 12.6 + 15.2 = 53
Yes!
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Answer:
x = 25.2
y = 12.6
z = 15.2