You labeled the triangle wrong sides 'a' and 'b' are supposed to be the sides that make the right angle. the other side is called the hypotenuse which is the longest side which you should have labeled 'c'
so Pythagorean theorem says a^2+b^2=c^2 so (2x+1)^2+(11x+5)^2=(12x+1)^2 distribute (4x^2+4x+1)+(121x^2+110x+25)=(144x^2+24x+1) add like terms 125x^2+114x+26=144x^2+24x+1 subtract 125x^2 from both sides 114x+26=19x^2+24x+1 subtract 114x from both sides 26=19x^2-90x+1 subtract 26 from both sides 0=19x^2-90-25 factor (x-5)(19x+5)=0 therefor x-5=0 and/or 19x+5=0 so x-5=0 add 5 to both sides x=5 19x+5=0 subtract 5 from both sides 19x=-5 divide both sides by 19 x=-5/19 since side legnths can't be negative, we can cross this solution out
so x=5 subtitute 1+2x 1+2(5) 1+10=11 side a=11
11x+5 11(5)+5 55+5=60 side b=60
12x+1 12(5)+1 60+1=60 side c=61 add them all up side a+b+c=11+60+61=132=total legnth
