Multiple choice

Triangle $ABC$ is a right triangle with sides of length $4, 6$ and $x$. If $4 < x < 6$, what is the approximate value of $x$?

  1. $4$
  2. $4.47$
  3. $5.21$
  4. $5.63$
  5. $7.21$
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B Correct answer
Explanation

In a right triangle with sides 4, 6, and x, x is either a leg or the hypotenuse. If x is a leg, x^2 + 4^2 = 6^2 => x^2 = 36-16=20 => x = sqrt(20) approx 4.47. If x is the hypotenuse, 4^2 + 6^2 = x^2 => 16+36=52 => x = sqrt(52) approx 7.21. Given 4 < x < 6, 4.47 is the correct value.

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