If in ΔABC, AB = 5 cm, BC = 12 cm and AC = 13 cm, then the length of the median BE is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6.5 cm
The sides fit Pythagoras’ theorem, so the triangle is right-angled. In a right triangle the mid-point of the hypotenuse is equally far from all three vertices (it is the centre of the circle through them), so the median to the hypotenuse is half the hypotenuse.
\(AB^2+BC^2=25+144=169=13^2=AC^2\), so \(\angle B=90^\circ\) and AC is the hypotenuse
BE is the median from B, so E is the mid-point of AC
\(BE=\displaystyle\frac{AC}{2}=\frac{13}{2}=6.5\,\mathrm{cm}\)
Tip: Worth memorising: in any right triangle, the median to the hypotenuse is half the hypotenuse.