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Medians of ΔABC intersect at G. If ar (ΔABC) = 27 cm2, then ar (ΔBGC) = - Mathematics

MCQ

Medians of ΔABC intersect at G. If ar (ΔABC) = 27 cm2, then ar (ΔBGC) =

Options

  • 6 cm2

  •  9 cm2

  • 12 cm2

  •  18 cm2

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Solution

Given: (1) Median of ΔABC meet at G.

(2) Area of ΔABC = 27 cm2

To find: Area of ΔBCG.

We know that the medians of the triangle divides each other in the ratio of 2:1

Hence,

ar (ΔBED) = `1/2 xx BC xx GD`

ar (ΔBED) =`1/2 xx BC xx 1/3 (AD)`

ar (ΔBED) =`1/3(1/2xx AD xx BC)`

ar (ΔBED) =`1/3 (Δ ABC)`

ar (ΔBED) = = `1/3(27)`

ar (ΔBED) == 9 cm2

 

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Q 11 | Page 61
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