Question 1114771
your triangle is right angle triangle

one leg is {{{12}}}, the other leg is {{{9}}}, so you use Pythagorean theorem to find the length of the hypotenuse {{{c}}}

{{{c^2=12^2+9^2}}}

{{{c^2=144+81}}}

{{{c^2=225}}}

{{{c=sqrt(225)}}}

{{{c=15}}}->the hypotenuse


since one leg is {{{12}}}, the other leg is {{{9}}}, on the leg (length{{{12}}}) one part {{{x}}}, than the other part is {{{12-x}}}


now use proportion:

{{{15:(12-x)=9:x}}}....solve for {{{x}}}

{{{15x=(12-x)9}}}

{{{15x=108-9x}}}

{{{15x+9x=108}}}

{{{24x=108}}}

{{{x=108/24}}}

{{{x=4.5}}}