Question

Find the length of side x in simplest radical form with a rational denominator.

Answer 1

Answer:  $2\sqrt{5}$

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Explanation:

Both legs are the same length, as indicated by the tickmark.

• a = $\sqrt{10}$
• b = $\sqrt{10}$
• c = x

Use the pythagorean theorem to solve for x

$a^2+b^2 = c^2\\\\( \sqrt{10} )^2 + ( \sqrt{10} )^2 = x^2\\\\10 + 10 = x^2\\\\x^2 = 20\\\\x = \sqrt{20}\\\\x = \sqrt{4*5}\\\\x = \sqrt{4}*\sqrt{5}\\\\x = 2\sqrt{5}$