Attempt this Geometry based Question of the Day of 22 November 2021

Question of The Day22-11-2021

In △ ABC, G is the centroid, AB = 12 cm, BC = 10 cm and CA = 14 cm, then what is the value (in cm) of GD?

QOTD 22 Nov

Answer

Correct Answer : c ) 8 cm

Explanation :

According to the question

AB = c = 12 cm, BC = a = 10 cm and CA = b = 14 cm

AD is the median

We know that

median=\({1 \over 2}{\sqrt{ 2b^2+2c^2-a^2}}\)

Median=\({1 \over 2}{\sqrt{ 2(12)^2+2(14)^2-(10)^2}}\)

⇒Median=\({1 \over 2}{\sqrt{ 288+392-100}}\)

Since, \({\sqrt {580}} \) ≅ 24

⇒Median=\({1\over 2}*{\sqrt {580}}\)= \({1\over 2}*24\)

⇒ 12 cm

Centroid divides Median in the ratio 2 : 1

⇒GD=\({1 \over 3}*12\)

⇒ GD = 4 cm

Hence, (c) is the correct answer.

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