Question

Help plz,BIG POINTS,also plz show me the steps as best as possible

Answer 1

Answer:

The correct answer is option 3.

Step-by-step explanation:

Given : ΔPQR, QM is altitude of the triangle

PM  = 8

MR = 18

To find = QM

Solution :

PR = 8 + 18  = 26

Let, PQ = x  , QR = y, QM = z

Applying Pythagoras Theorem in ΔPQR

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

$x^2+y^2=(26)^2$..[1]

Applying Pythagoras Theorem in ΔPQM

$PM^2+QM^2=PQ^2$

$8^2+z^2=(x)^2$..[2]

Applying Pythagoras Theorem in ΔQMR

$MR^2+QM^2=QR^2$

$18^2+z^2=(y)^2$..[3]

Putting values of $x^2$ and $y^2$ from [2] and [3 in [1].

$8^2+z^2+18^2+z^2=(26)^2$

$2z^2=(26)^2-(8)^2-(18)^2$

$2z^2=288$

$z^2=144$

z = ±12

z = 12 = QM ( ignoring negative value)

The length of QM is 12.