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Tell whether the following statement is true or false:

The base BC of triangle ABC is divided at D such $B D = 12 D C$ . Then area of triangle ABD = $13$ area of triangle ABC.

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True

False

answer is A.

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Detailed Solution

Given the base BC of triangle ABC is divided at D such

B D = 12 D C

Therefore, DC = 2BD.
Now in triangle ABC,
BC = BD + CD
BC = BD + 2BD
BC = 3BD

Area of triangle ABC is,

= 12 × BC × AE

Area of triangle ABD is,

= 12 × BD × AE

As,

= 12 × 13 × BC × AE

Area of triangle ABD =

13

area of triangle ABC.
The given statement is true.
Hence, option 1 is correct.

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