Question 946673
You're right.
We define a variable:
{{{x}}}= length of second .leg.
:{{{x-7}}}= length of second leg;
{{{x+1}}}= length of hypotenuse.
We apply the Pythagorean theorem:
{{{x^2(x-7)^2=(x+1)^2)))
{{{x^2+x^2-14x+49=x^2+2x+1}}}
{{{cross(x^2)+x^2-14x+49=cross(x^2)+2x+1}}}
{{{x^2-14x+49=2x+1}}}
{{{x^2-14x-2x+49-1=2x+1-2x-1}}
{{{x^2-16x+48=0}}
We solve by factoring:
{{{x^2-16x+48=0}}}<--->{{{(x-4)(x-12)=0}}}--->{{{system(x-4=0,"or",x-12=0)}}}--->{{{system(x=4,"or",x=12)}}} 
{{{x=4}}}<--->{{{x-7=4-7}}}<--->{{{x-7=-3}}} does not work, because it yields a negative number for the length of the first leg.
{{{x=12}}}--->{{{system(x=12,x-7=12-7,x+1=12+1)}}}--->{{{highlight(system(x=12,x-7=5,x+1=13)))}}}