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olya-2409 [2.1K]
3 years ago
5

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

Mathematics
1 answer:
Len [333]3 years ago
6 0

we know the triangle is an isosceles, so it has twin sides, and then the hypotenuse, since it's a right-triangle, we can just use the pythagorean theorem for that.


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

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