In right-angled triangle ABC, ∠C=90, CM is perpendicular on AB. If AB = 18 cm and BM = 6 cm, then find the length of CM.

Correct option is A

Given:

Triangle ABC is a right-angled triangle with ∠C = 90°.

CM is perpendicular to AB.

AB = 18 cm, BM = 6 cm.

Formula Used:

CM$$^2$$​ = BM $$\times$$​ AM
AM = AB − BM

Solution:

AB = 18 cm, BM = 6 cm, so AM=18−6=12 cm

Apply the altitude-on-hypotenuse theorem:

CM$$^2$$​ = BM $$\times$$​AM = 6 $$\times$$​12 = 72

CM = $$\sqrt{72} = 6\sqrt{2} \, \text{cm}$$​​