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?
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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