Question

The hypotenuse of a 45-45-90 triangle has a length of 10 units. What is the length of one of its legs?

Answer 1

if \[10=a \sqrt{2}\]
find a

divide both sides by square root of 2,
\[10\div \sqrt{2}=a \sqrt{2} \div \sqrt{2}\]
the squrae roots on the right side cancel,
\[\frac{10}{\sqrt{2}}=a\] this is not an answer yet, since you can't have a radical in a denominator,
\[\frac{10\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}\]\[--->\frac{10\sqrt{2}}{2}--->5\sqrt{2}\]