If the length of one leg of a right triangle is 16 and the length of the hypotenuse is 2 more than the length of the other leg, what are the lengths of all the sides of the triangle? other leg = a0 hypotenuse = a1

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The lengths of the sides of the triangle are 16, 63, and 65.

a0 = 63
a1 = 65


You have
.. a0² +16² = a1²
You want
.. a1 = a0 +2
so
.. a0² +256 = (a0 +2)² = a0² +4a0 +4 . . . . substitute and expand
.. 252 = 4a0 . . . . . . . . . subtract a0² +4
.. 63 = a0 . . . . . . . . . . . .divide by 4
.. a1 = 63 +2 = 65