Multiple choice

What is the length, in feet, of the hypotenuse of a right angled triangle with the lengths of its perpendicular sides as $6$ feet long and $7$ feet, respectively?

  1. $\displaystyle \sqrt { 13 } $
  2. $\displaystyle \sqrt { 85 } $
  3. $13$
  4. $21$
  5. $42$
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B Correct answer
Explanation

By the Pythagorean theorem, the hypotenuse c is sqrt(a^2 + b^2). Here, c = sqrt(6^2 + 7^2) = sqrt(36 + 49) = sqrt(85).

AI explanation

Apply the Pythagorean theorem to find the hypotenuse of a right-angled triangle by taking the square root of the sum of the squares of the two perpendicular sides. Calculate the sum of the squares as 6 squared plus 7 squared, which is 36 plus 49, yielding a total of 85. The length of the hypotenuse is therefore the square root of 85.

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