In triangle PQR, two medians, PS and QT, intersect each other at X at right angles. If PS = 18 cm and QT = 7.5 cm, then find the length of PQ.
Show answer & explanation
Correct answer: C
Explanation
Given:
PS = 18 cm
QT = 7.5 cm
The medians intersect at right angles at X.
Median:
PX = (2/3)PS
QX = (2/3)QT
If the medians are at right angles, then
PQ² = PX² + QX²
PX = (2/3) × 18 = 12
QX = (2/3) × 7.5 = 5
PQ² = 12² + 5²
PQ² = 14² + 25
PQ² = 16²
PQ = 13 cm