SOLUTION: 1) the lengths of the three sides of a rigt angled triangle are x-2, 2x, and x+6. x+6 is the longest side of the triangle. what is the length of the shortest side of the triangle?

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Question 329728: 1) the lengths of the three sides of a rigt angled triangle are x-2, 2x, and x+6. x+6 is the longest side of the triangle. what is the length of the shortest side of the triangle?
2) th diference betwen two positive number is 3. the difference between their reciprocals is 1/90. what are the two numbers? (Note: the reciprocal of x is 1/x)
Answer by Alan3354(69443) (Show Source):
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1) the lengths of the three sides of a rigt angled triangle are x-2, 2x, and x+6. x+6 is the longest side of the triangle. what is the length of the shortest side of the triangle?

x = 2 � 4sqrt(3)
x-2 = +4sqrt(3) the shortest side
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2) th diference betwen two positive number is 3. the difference between their reciprocals is 1/90. what are the two numbers? (Note: the reciprocal of x is 1/x)
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Thx for the info on reciprocals.
x is the larger number.
x - y = 3
1/x - 1/y = -1/90 (minus because the recip of a larger # is smaller)
Multiply by 90xy
90y - 90x = -xy
x = y+3, sub for x
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90y - 90*(y+3) = -y*(y+3) = -y^2 - 3y
y^2 + 3y = 270
y^2 + 3y - 270 = 0
(y + 18)*(y - 15) = 0
y = 15
x = 18