Question

In ΔPQR, ∠Q=90°, PQ=12, QR=5 and QS is a median. Find L(QS).

Answer 1

Answer:

L(QS) = 6.5

Step-by-step explanation:

In ΔPQR, ∠Q=90°, PQ=12, QR=5

PR² = PQ² + QR²  (using Pythagoras theorem)

=> PR² = 12² + 5²

=> PR² = 169

=> PR = 13

QS is median

=> PS = RS = 13/2 = 6.5 cm

in ΔPQR  

Cos ∠P  = PQ/PR  = 12 /13

in Δ PQS

QS² = PQ² + PS² - 2*PQ*PSCos∠P

=> QS² = 12² + 6.5² - 2 * 12 * 6.5 * (12/13)

=> QS² = 12² + 6.5² - 12²

=> QS² = 6.5²

=> QS = 6.5

L(QS) = 6.5

Answer 2

Answer:

6.5

Step-by-step explanation:

Let:

ΔPQR is a Right angle triangle:

Where,

Q=Right angle triangle

PQ=12

QR=5

Now:

In ΔPQR:

So PQ and QR are the sides and PR is the hypotenuse of ΔPQR

By using Pythagoras theorem:

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

$PR^{2} =(12)^{2}+(5)^{2}$

=144+25

=169

PR=13

Length of hypotenuse Right- angled triangle=13

We know that:

The length of the median of hypotenuse =$\dfrac{1}{2}$×Length of the hypotenuse

Length of the median of hypotenuse =$\dfrac{1}{2}$×13

=6.5

=Length of the median of its hypotenuse=6.5