The given triangle has Centroid at O-If PC -54 cm- Find the length of OC-A- 24 cmB- 36 cmC- 18 cmD- 42 cm

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Standard VIII

Mathematics

Ratio in Which Centroid Divides Median

The given tri...

Question

The given triangle has Centroid at O.

If PC = 54 cm, Find the length of OC.

18 cm

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24 cm

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36 cm

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42 cm

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Solution

The correct option is C
36 cm

PC is a Median and O is the centroid.

Centroid Divides Median in the Ratio 2 : 1.

OC : OP = 2 : 1

OC = 2x and OP = x

PC = OC + OP = 2x + x = 3x

3x = 54

$\Rightarrow$ x = 18 cm

$∴$ Length of OC = 2x = 2 $\times$ 18 = 36 cm

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The given triangle has Centroid at O. If PC = 54 cm, Find the length of OC.

The correct option is C 36 cm PC is a Median and O is the centroid. Centroid Divides Median in the Ratio 2 : 1. OC : OP = 2 : 1 OC = 2x and OP = x PC = OC + OP = 2x + x = 3x 3x = 54 ⇒ x = 18 cm ∴ Length of OC = 2x = 2 × 18 = 36 cm

The given triangle has Centroid at O.

If PC = 54 cm, Find the length of OC.

The correct option is C
36 cm

PC is a Median and O is the centroid.

Centroid Divides Median in the Ratio 2 : 1.

OC : OP = 2 : 1

OC = 2x and OP = x

PC = OC + OP = 2x + x = 3x

3x = 54

$\Rightarrow$ x = 18 cm

$∴$ Length of OC = 2x = 2 $\times$ 18 = 36 cm