Question 1182033
the hypotenuse of a right triangle is {{{6cm}}}. =>{{{c=6}}}

One side is {{{2cm}}} longer than the other. =>{{{a=b+2}}}

Find the length of the two sides of this right-angle triangle

{{{c^2=a^2+b^2}}}......substitute given

{{{6^2=(b+2)^2+b^2}}}

{{{36=b^2+4b+4+b^2}}}

{{{36=2b^2+4b+4}}}...simplify

{{{18=b^2+2b+2}}}

{{{b^2+2b+4-18=0}}}

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

using quadratic formula you get:

{{{b = -1 - sqrt(17)}}}=>disregard negative solution
{{{b = -1 + sqrt(17)}}}
{{{a=-1 + sqrt(17)+2}}}=>{{{a=1 + sqrt(17)}}}

or approximately:
{{{b=3.12310562561766}}}
{{{a=3.12310562561766+2}}}=> {{{a=5.12310562561766}}}