The sides of a triangle are 3 cm, 4 cm and 5 cm. What is the sum of the squares of its three medians?

Think it through first, then pick an option.

Answer and explanation

Correct answer: d 37.5 sq cm

The squares of the sides add to 9 + 16 + 25 = 50 and the squares of the medians add to ¾ × 50 = 37.5.

Why the other options are wrong

a 83.5 sq cm: 83.5 does not come out; ¾ × (9 + 16 + 25) = 37.5.
b 75.5 sq cm: 75.5 does not come out; the squares of the medians add to ¾ × 50 = 37.5, not double that.
c 47.5 sq cm: 47.5 does not follow from any formula; d² + e² + f² = ¾ × 50.