Question 165934
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{{{shorter_leg=x}}} ---> let's point it as the adjacent side
{{{x+2}}} -------------> let's point it as the oppposite side
{{{x+4}}} -------------> hypotenuse side
differ by 2cm --{{{system(x=adj,x+2=opp)}}}
By Pyth. Theorem:
{{{(x+4)^2=x^2+(x+2)^2}}}
{{{x^2+8x+16=x^2+x^2+4x+4}}}
{{{2x^2+4x+4-x^2-8x-16=0}}}
{{{x^2-4x-12=0}}}, perfect square, factorable
{{{(x-6)(x+2)=0}}}
2 values ---{{{system(highlight(x=6),x=-2)}}}
As highlighted, shortest side: adj= 6cm; opp=6+2=8cm; hyp=6+4=10cm
See below,
{{{drawing(300,300,-5,10,-5,10,graph(300,300,-5,10,-5,10),(green(line(6,0,0,0))),(blue(line(6,0,6,8))),(red(line(6,8,0,0))))}}} {{{system(green=adjacent=6cm,blue=opposite=8cm,red=hypotenuse=10cm)}}}
check:
{{{10^2=6^2+8^2}}}
{{{100=36+64}}}
{{{100=100}}}
Thank you,
Jojo</pre>