Question

in triangle pqr if the length of PQ is equal to 24 cm PR is equal to 30 cm and QR is equal to 40 cm if PS is the median then the length of PS will be

Answer 1

Given: A triangle PQR in which PQ = 24 cm, PR=30 cm, and QR=40 cm and PS is median on the side QR.

To find: Length of PS

Solution: As we know in a triangle sum of two sides is always greater than third side.

Let length of median = x cm

In Δ PQS

QS + SP>PQ

20 + x > 24

x > 24 -20

x> 4.................(1)

also , PQ+QS > PS

24 +20 > x

x< 44..........(2)

In Δ PSR

PS +SR>PR

x+20>30

x>30-20

x>10...............(3)

Also, PR+ RS>PS

30+20>x

x<50...............(4)

Combining (1),(2),(3),and (4) we get i.e x>4 and x>10 and x<44 and x<50

x>10 and x<44.

The value of median will lie , 10<Median<44.