In ∆ABC, AB = 3 cm, AC = 4 cm and BC = 5 cm. What is the length of AD, if D is the midpoint of side BC?
Explanation:
Since D is the midpoint of BC ⇒ AD is the median to BC
Using Apollonius theorem, we get
AB2 + AC2 = 2 × (AD2 + BD2)
∴ 32 + 42 = 2 × (AD2 + BD2)
∴ AD = 9+162-6.25 = 12.5-6.25 = 6.25 = 2.5 cm
Alternately,
The sides of the given triangle form a pythagorean triplet.
∴ The given triangle is a right triangle with BC as the hypotenuse.
Since D is the midpoint of the hypotenuse, D is the circum-center of the right triangle hence D is equidistance from all three vertices.
In a right triangle, circumradius = half of the hypoteneuse.
∴ DA = DB = DC = 5/2 = 2.5 cm.
Hence, option (c).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.