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
[tex]PQ^2+QR^2=PR^2[/tex]
[tex]x^2+y^2=(26)^2[/tex]..[1]
Applying Pythagoras Theorem in ΔPQM
[tex]PM^2+QM^2=PQ^2[/tex]
[tex]8^2+z^2=(x)^2[/tex]..[2]
Applying Pythagoras Theorem in ΔQMR
[tex]MR^2+QM^2=QR^2[/tex]
[tex]18^2+z^2=(y)^2[/tex]..[3]
Putting values of [tex]x^2[/tex] and [tex]y^2[/tex] from [2] and [3 in [1].
[tex]8^2+z^2+18^2+z^2=(26)^2[/tex]
[tex]2z^2=(26)^2-(8)^2-(18)^2[/tex]
[tex]2z^2=288[/tex]
[tex]z^2=144[/tex]
z = ±12
z = 12 = QM ( ignoring negative value)
The length of QM is 12.
