Question

QID: 24 - PQR is a triangle such that PQ = PR. RS and QT are the median to the sides PQ and PR respectively. If the medians RS and QR intersect at right angle,then what is the value of (PQ/QR)

Answer 1

Answer:

$\frac{PQ}{QR} = \sqrt[]{\frac{5}{2} }$

Step-by-step explanation:

Given PQR is an isoceles triangle (PQ=PR). Also given that RS and QT are medians to the Sides PQ and PR respectively.

The condition is that the medians intersect each other at right angles

According the theorem when medians intersect each other at 90° in an isosceles triangle

$PQ^{2} +PR^{2} = 5 QR^{2}$

now PQ= PR

⇒2PQ^2= 5QR^2

⇒$\frac{PQ}{QR} = \sqrt[]{\frac{5}{2} }$