Question

I’m trying to find x for length on a triangle that has 4 sides 6 total because 2 sides are together, I have only 3 sides those are, 5 mm, 13 mm, 35 mm, then x what is it?

Answer 1

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=√(c^2 - a^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{5}\\ o=\stackrel{opposite}{y} \end{cases} \\\\\\ y=√( 13^2 - 5^2)\implies y=√( 169 - 25 ) \implies y=√( 144 )\implies y=12 \\\\[-0.35em] ~\dotfill`

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{35}\\ o=\stackrel{opposite}{12} \end{cases} \\\\\\ x=√( 35^2 + 12^2)\implies x=√( 1225 + 144 ) \implies x=√( 1369 )\implies \boxed{x=37}`