The three medians of a right triangle are 6, 7 and 8 units. What is the length of the hypotenuse in units?

Correct answer: b 9.97 (about)

From 2(d² + e² + f²) = 3c², c² = ⅔ × (36 + 49 + 64) = 99.33, c ≈ 9.97.

Why the other options are wrong

• a 9.00: For 9, 2(36 + 49 + 64) = 298 ≠ 3·81 = 243; the hypotenuse satisfies c² = ⅔ × 149.
• c 14.28 (about): 14.28 comes from a wrong factor; multiply 149 by ⅔ and take the root.
• d 14.95 (about): 14.95 = √223.5 comes from 1.5 × 149 (using 3/2 for c² is the wrong way round); the correct factor is ⅔.