Question

In the figure shown below, PQ is a median of PRS, PS = 4cm, and SQ = 3 cm. What is PR?

Answer 1

Given:

PQ is a median of ΔPRS.

PS = 4 cm

SQ = 3 cm

To find:

The side length PR.

Solution:

PQ is a median of ΔPRS.

⇒ SQ = QR

⇒ QR = 3 cm

SR = SQ + QR

= 3 + 3

SR = 6 cm

Using Pythagoras theorem:

In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.

`PR^2=PS^2+SR^2`

`PR^2=4^2+6^2`

`PR^2=16+36`

`PR^2=52`

Taking square root on both sides.

PR = 7.2 cm

Therefore PR is 7.2 cm.