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In a right triangle with integer length sides, the hypotenuse has length 39 units. How many units is the length of the shorter leg?

tertre  Dec 28, 2017
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 #1
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39^2 - 36^2 = 15^2

So, the shorter side = 15 units.

Guest Dec 28, 2017
edited by Guest  Dec 29, 2017
 #2
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Notice that  one possible  "Pythagorean Triple" right triangle is  one with the sides  5 - 12 - 13

 

Any any  multiple  of these will also be a Pythagorean Triple...so....this implies that

 

5(3)  -  12(3)  - 13(3)   =

 

15  -  36   -  39   will also be a Pythagorean Triple

 

So....the shorter leg  =  15 units

 

 

cool cool cool

CPhill  Dec 29, 2017

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