Question

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

Answer 1

Answer:
`2√(5)`

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Step-by-step explanation:

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

• a =
  `√(10)`
• b =
  `√(10)`
• c = x

Use the pythagorean theorem to solve for x

`a^2+b^2 = c^2\\\\( √(10) )^2 + ( √(10) )^2 = x^2\\\\10 + 10 = x^2\\\\x^2 = 20\\\\x = √(20)\\\\x = √(4*5)\\\\x = √(4)*√(5)\\\\x = 2√(5)\\\\`