Question

in triangle PQR angle Q : angle R : angle P =1:2:1. if PQ = 2 root 6 then PR =

Answer 1

Answer:

PR =✓6

Step-by-step explanation:

In triangle PQR ,

<Q : <R :<P = 1:2:1

Let <Q = 1x

So, <R =2x and <P = 1x

We know

<Q+<R+<P=180° ( angle sum property of triangle)

=>1x+2x+1x=180°

=> 4x = 180°

=> x = 180°÷4

= 45°

So,the angles of the triangle are 45°, 2×45°,45°

i.e 45° , 90° 45°

So , the triangle is a isosceles right angled triangle.

and <R =90° , <P =45° and <Q =45° and QR = PR

According to Pythagoras theorem

PQ^2 = QR^2+PR^2

=> (2✓6)^2 = PR^2+PR^2

=>4×6 = 2PR^2

=>PR^2=12/2

=>PR = ✓6