Question 1153637


if one leg of a right triangle is {{{7cm}}} shorter than the other leg, we have

{{{a=b+7}}}

if the hypotenuse is at least {{{13cm}}}, then

{{{a^2+b^2=13^2}}}....substitute {{{a}}}

{{{(b+7)^2+b^2=13^2}}}

{{{b^2+14b+49+b^2=169}}}

{{{2b^2+14b+49-169=0}}}

{{{2b^2+14b-120=0}}}

{{{b^2+7b-60=0}}}.....factor

{{{b^2+12b-5b-60=0}}}

{{{(b^2+12b)-(5b+60)=0}}}

{{{b(b+12)-5(b+12)=0}}}

{{{(b - 5) (b + 12) = 0}}}

=> {{{b=5}}} or {{{b=-12}}}->disregard negative solution

so, {{{a=b+7}}}->{{{a=5+7}}}->{{{a=12}}}