Question

A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the​ triangle?

Answer 1

Since it's a right triangle

$\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ -------\\ c=8\\ b=a \end{cases}\implies 8^2=a^2+a^2 \\\\\\ 64=2a^2\implies \cfrac{64}{2}=a^2\implies 32=a^2\implies \sqrt{32}=a \\\\\\ \sqrt{16\cdot 2}=a\implies \sqrt{4^2\cdot 2}=a\implies 4\sqrt{2}=a$