11990 perimeter RT

A right triangle has integer side lengths and a perimeter of 11990. In addition, we know that one of its perpendiculars has a prime number length. Find its length.

Correct answer:

a =  109

Step-by-step explanation:

o=11990 o=a+b+c=11990=2×5×11×109 a a+b b=c c a a+b b=(11990ab)2 a2+b2=14376010023980 a+a223980 b+2 ab+b2 23980 a+23980 b=143760100+2 ab  a=109  23980 a+23980 b=143760100+2 a b 23980 109+23980 b=143760100+2 109 b  23762b=141146280  b=23762141146280=5940  b=5940  c=oab=119901095940=5941

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