Then The Triangle will be : If

If the median drawn on the base of a triangle is half its base, then the triangle will be


  1. obtuse angled
  2. equilateral
  3. right angled
  4. acute angled
Anurag Mishra Professor Asked on 1st August 2015 in Maths.
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Answer: (3) Right angled triangle
Let PQR be the triangle PO be the median.Then, PO = QR/2

By Apollonius theorem,

(PQ)2 + (PR)2 = 2 (PO2 + OQ2)
PO = OQ = OR = QR/2
Therefore, PQ2 + PR2 = 2[(QR/2)2 + (QR/2)2]

PQ2 + PR2 = 2(QR2/4 + QR2/4)

PQ2 + PR2 = 2(QR2/2)
PQ2 + PR2 = QR2
It follows Pythagoras theorem.
Hence, it is a right angled triangle.

Anurag Mishra Professor Answered on 1st August 2015.
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