Multiple choice

(\triangle PQR) is an isosceles triangle with (PQ = PR = 25) cm. If (PS) is the median on (QR) from (P) such that (PS = 7) cm, then the length of (QR) is in cm :

  1. 42

  2. 48

  3. 35

  4. 28
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In isosceles triangle PQR with PQ = PR, the median PS is also the altitude. Using Apollonius's theorem or Pythagorean theorem: PS² + (QR/2)² = PQ². Therefore (QR/2)² = 25² - 7² = 625 - 49 = 576, so QR/2 = 24 and QR = 48 cm. The median from the apex in an isosceles triangle bisects the base perpendicularly.

Keep practicing — related questions