Question 165568
Call the smaller leg {{{x}}}
Call the hypotenuse {{{h}}}
The longer leg = {{{x+14}}}
{{{h = x + 16}}}
{{{h^2 = x^2 + (x+14)^2}}}
{{{(x+16)^2 = x^2 + x^2 + 28x + 196}}}
{{{x^2 + 32x + 256 = 2x^2 + 28x + 196}}}
{{{x^2 - 4x - 60 = 0}}}
You can solve by completing the square
{{{x^2 - 4x + (4/2)^2 = 60 + (4/2)^2}}}
{{{x^2 - 4x + 4 = 64}}}
{{{(x - 2)^2 = 8^2}}}
Take the square root of both sides
{{{x - 2 = 8}}}
{{{x = 10}}}
{{{x + 14 = 24}}}
{{{x + 16 = 26}}}
The sides are 10,24, and 26
check answer
{{{h^2 = x^2 + (x+14)^2}}}
{{{26^2 = 10^2 + 24^2}}}
{{{676 = 100 + 576}}}
{{{676 = 676}}}
OK