ABC is a triangle right angled at B. Let D be the midpoint on AC. If BD=6.5 cm, then what is AB^2+BC^2 equal to?

Explanation

In a right-angled triangle, the median to the hypotenuse is exactly half the length of the hypotenuse. Thus, AC = 2 \times BD = 2 \times 6.5 = 13 cm. By Pythagoras' theorem, AB^2 + BC^2 = AC^2 = 13^2 = 169 square cm.

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