I am having trouble with this problem. I need to find the lengths of this right triangle. How would you do this?

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

Answered by apologiabiology | 2024-06-10

To find the lengths of the sides of a right triangle, use the Pythagorean theorem: a 2 + b 2 = c 2 . Identify the sides, substitute known values, and solve for the unknown side. Ensure to remember that the hypotenuse is the longest side opposite the right angle.
;

Answered by apologiabiology | 2024-12-26