Question

Find the perimeter of the shape below (it’s not drawn to scale)

Answer 1

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".

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2-b^2)=a \qquad \begin{cases} c=\stackrel{hypotenuse}{26}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{24}\\ \end{cases} \\\\\\ √(26^2-24^2)=x\implies √(100)=x\implies \boxed{10=x}`

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.

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2-b^2)=a \qquad \begin{cases} c=\stackrel{hypotenuse}{26}\\ a=\stackrel{adjacent}{y}\\ b=\stackrel{opposite}{25}\\ \end{cases} \\\\\\ √(25^2-24^2)=y\implies √(49)=y\implies \boxed{7=y}`

`\bf perimeter\implies 25+\stackrel{x}{10}+26+\stackrel{x}{10}+\stackrel{x}{10}+\stackrel{y}{7}\implies 88`