The legs of an isosceles triangle are congruent. Since the perimeter is the sum of the three side lengths, we write:

x+(2x−6)+(2x−6)=53

Solve for x: 5x−12=53

5x=65

\(\displaystyle{x}=\frac{{65}}{{5}}\)

x=13

x+(2x−6)+(2x−6)=53

Solve for x: 5x−12=53

5x=65

\(\displaystyle{x}=\frac{{65}}{{5}}\)

x=13