Question 176110This question is from textbook
: If the length of the sides of a right triangle are consecutive multiples of three, then what is the hypotenuse
I got that the sides were 3x and 3x+3 and with the pythagorean theorem, I got an equation 18x(squared)+18x+9=c(squared)
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If the length of the sides of a right triangle are consecutive multiples of three, then what is the hypotenuse?
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side 1: 3x
side 2: 3(x+1)
side 3: 3(x+2)
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[3(x+2)]^2 = [3(x+1)]^2 + [3x]^2
Divide thru by 9 to get:
(x+2)^2 = (x+1)^2 + x^2
x^2 + 4x + 4 = x^2 + 2x + 1 + x^2
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x^2 -2x -3 = 0
(x-3)(x+1) = 0
Positive solution:
x = 3
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1st: 3*3 = 9
2nd: 3*4 = 12
3rd: 3*5 = 15
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Is it a right triangle?
15^2 = 12^2 + 9^2
225 = 144 + 81
true
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Cheers,
Stan H.
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