Question 998362
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In a triangle f, the shorter leg is 1 less than one-third of the longer leg while the hypotenuse is 1 more then the longer leg. 
Find the measures of the legs and the hypotenuse.
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{{{(x/3-1)^2}}} + {{{x^2}}} = {{{(x+1)^2}}},  (x is the shorter leg measure)


{{{x^2/9}}} - {{{(2/3)x}}} + {{{1}}} + {{{x^2}}} = {{{x^2 + 2x + 1}}}, -----> multiply by 9 both sides ----->


{{{x^2 - 2*3x + 9}}} + {{{9x^2}}} = {{{9x^2 + 18x + 9}}}, 


{{{x^2 - 24x}}} = {{{0}}},


x = 24.


Check that the solution is correct.
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