Check the picture below.
so let's notice, the green triangle and the red one, both have a hypotenuse of 26 and a side of 24, so the missing side must be the same, namely "x".
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{26}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{24}\\ \end{cases} \\\\\\ \sqrt{26^2-24^2}=x\implies \sqrt{100}=x\implies \boxed{10=x}[/tex]
now, let's inspect the triangle on the left-hand-side, let's see, it has a hypotenuse of 25, and a side of 24.
[tex]\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{26}\\ a=\stackrel{adjacent}{y}\\ b=\stackrel{opposite}{25}\\ \end{cases} \\\\\\ \sqrt{25^2-24^2}=y\implies \sqrt{49}=y\implies \boxed{7=y}[/tex]
[tex]\bf perimeter\implies 25+\stackrel{x}{10}+26+\stackrel{x}{10}+\stackrel{x}{10}+\stackrel{y}{7}\implies 88[/tex]
