Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. Given = 3√(2) ________ inches.

Question

Find the hypotenuse of each isosceles right triangle when the legs are of the given measure.

Given =
`3√(2)`

________ inches.

Answer 1

`\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=√(a^2+b^2) \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{3√(2)}\\ b=\stackrel{opposite}{3√(2)}\\ \end{cases} \\\\\\ c=\sqrt{(3√(2))^2+(3√(2))^2}\implies c=\sqrt{3^2√(2^2)+3^2√(2^2)}\implies c=√(18+18) \\\\\\ c=√(36)\implies c=6`