Multiple choice

A right-angles triangle has hypotenuse $13$ cm, one side is $12$ cm, then the third side is _________.

  1. $5$ cm
  2. $6$ cm
  3. $7$ cm
  4. $4$ cm
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A Correct answer
Explanation

By the Pythagorean theorem, a^2 + b^2 = c^2. Given c=13 and a=12, then b^2 = 13^2 - 12^2 = 169 - 144 = 25. Thus, b = 5.

AI explanation

Using the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides. We set up the equation 13 squared equals 12 squared plus the third side squared, resulting in 169 equals 144 plus the third side squared. Subtracting 144 from 169 leaves 25, and the square root of 25 is 5 cm.

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