SOLUTION: The measures of the sides of a right triangle are those of a Pythagorean triple. If the measure of the shortest side is 17, what are the measures of the other two sides?
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Question 276703: The measures of the sides of a right triangle are those of a Pythagorean triple. If the measure of the shortest side is 17, what are the measures of the other two sides?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
PPT = Primitive Pythagorean Triple.
The shortest leg in a PPT is always odd, so we know that 
. The other leg in a PPT is always 4 times a triangle number -- a triangle number being the sum of consecutive integers beginning at 1 and the 
th one being given by }{2})
, which multiplied by 4 is )
. And the hypotenuse is always 1 larger than the long leg, so \ +\ 1)
.
Since we know that , 
. Since , ((8)\,+\,1)\ =\ 16\,\cdot\,8\ =\ 144)
for the long leg and 
for the hypotenuse.
Check:
John
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