Question

If the hypotenuse of a 45°-45°-90° triangle is 13, what is the length of one of the legs?

Answer 1

Answer:

B

Step-by-step explanation:

It's right on Edge.

Answer 2

Answer:

  B.  (13√2)/2

Step-by-step explanation:

Let L represent the length of one leg of the triangle. We note that the triangle is isosceles, so both legs are the same length. Then the Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs:

  13² = L² + L²

  13² = 2L²

  13 = (√2)L

  L = 13/√2 = (13√2)/2 . . . length of one leg

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To "rationalize the denominator", we multiply the fraction 13/√2 by (√2)/(√2). The result is (13√2)/2.