Question 1133898
the sides of the right triangle. 
{{{(1/2)x}}} ->leg 
{{{x+3 }}}->hypotenuse
{{{x+2}}}->leg 


{{{(x+3 )^2=((1/2)x)^2+(x+2)^2}}}

{{{x^2+6x+9 =x^2/4+x^2+4x+4}}}...both sides multiply by {{{4}}}

{{{4x^2+24x+36 =x^2+4x^2+16x+16}}}

{{{4x^2+24x+36 -x^2-4x^2-16x-16=0}}}

{{{cross(4x^2)+24x+36 -x^2-cross(4x^2)-16x-16=0}}}

{{{8x+20 -x^2=0}}}..both sides multiply by {{{-1}}}

{{{x^2 -8x -20 =0}}}.........factor

{{{x^2 -10x +2x-20 =0}}}

{{{(x^2 -10x) +(2x-20) =0}}}

{{{x(x -10) +2(x-10) =0}}}

{{{(x - 10) (x + 2) = 0}}}

solutions:

{{{x=10}}}
{{{x=-2}}}-> disregard negative solution, we need the lengths of the sides



Find the lengths of the sides of the right triangle:
{{{x=10}}}
{{{(1/2)10}}}->{{{highlight(5)}}} ->leg 
{{{10+3 }}}->{{{highlight(13)}}}->hypotenuse
{{{10+2}}}->{{{highlight(12)}}}->leg