Question : In $\triangle {ABC} $, AB = 48 cm, BC = 55 cm and AC = 73 cm. If O is the centroid of the triangle, then the length (in cm) of BO (correct to one decimal place) is:
Option 1: 25.6
Option 2: 24.3
Option 3: 20.4
Option 4: 18.3
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Correct Answer: 24.3
Solution :
Since 48, 55, and 73 are triplets
$\triangle ABC$ is a right-angled triangle and $\angle B = 90^\circ$
We know that in a right-angled triangle,
Length of the median from the right-angled vertex = $\frac{\text{Length of hypotenuse}}{2}$
⇒ $BM = \frac{AC}{2} = \frac{73}{2}$
And we know that OB : OM = 2 : 1
$\therefore OB = \frac{2}{3} × \frac{73}{2}= 24.33$ cm
Hence, the correct answer is 24.3.
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