In ∆ABC, two medians AD and BE intersect at G at right angles. If AD = 12 cm and BE = 9 cm, then the length of AB is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 10 cm.
Given,
AD = 12 cm and BE = 9 cm
As shown in the figure, G is the centroid of triangle ABC and divides the median in 2 : 1 ratio.
Length of the segments from the centroid:
AG = 2/3 × AD = 2/3 × 12 = 8 cm
BG = 2/3 × BE = 2/3 × 9 = 6 cm
Using the Pythagorean theorem in ΔAGB
⇒ AB2 = AG2 + BG2
⇒ AB2 = 82 + 62 = 64 + 36
⇒ AB2 = 100
⇒ AB = 10 cm