If △ABC, D and E are the mid points of sides Bc and AC, respectively .If AD = 10.8cm, BE = 14.4 cm and AD and BE intersect at G at a right angle, then the area ( in cm2) of △ABC is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 103.68
Concept
Centroid divides median in the ratio of 2: 1
Centroid divides the trinagle in the 6 equal areas:
Application
D and E is the midpoint of BC so AD and BE is median respectively
Centroid always divide the median in 2 ∶ 1
AG = (2/3) × AD
⇒ AG = (2/3) × 10.8
⇒ AG = 7.2 cm
Similarly, BG = (2/3) × BE
⇒ BG = (2/3) × 14.4
⇒ BG = 9.6 cm
In ΔAGB,
∠AGB = 90°
area of ΔAGB = (1/2) × AG × BG
(1/2) × 9.6 × 7.2 = 34.56 cm2
Centroid divides the trinagle in the 6 equal areas:
So, area of ΔAGB = 2 units
2 units = 34.56 cm2
6 units = 34.56 x 3 = 103. 68 cm2
So, area trinagle ABC = 103. 68 cm2