In a triangle ABC, a line is drawn from C which bisects AB at point D. Find the ratio of the area of triangles DBC and ABC.a)1 1b)2 1c)1 2d)1 3Correct answer is option 'C'. Can you explain this answer?

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In a triangle ABC, a line is drawn from C which bisects AB at point D. Find the ratio of the area of triangles DBC and ABC.

a)
1 ∶ 1
b)
2 ∶ 1
c)
1 ∶ 2
d)
1 ∶ 3

Correct answer is option 'C'. Can you explain this answer?

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Verified Answer

In a triangle ABC, a line is drawn from C which bisects AB at point D....

As (6, 8, 10) is a pythagorean triplet so triangle ABC is a right angled triangle, right angled at B

⇒ Area of triangle ABC = (1/2) × base × height = 1/2 × 6 × 8 = 24 cm2

Now, point D bisects AB

⇒ DB = (1/2) × AB = 1/2 × 8 = 4 cm

Also, triangle DBC is a right angle triangle, right angle at B

⇒ Area of triangle DBC = (1/2) × base × height = 1/2 × 6 × 4 = 12 cm2

∴ Required ratio = area of triangle DBC ∶ area of triangle ABC = 12 ∶ 24 = 1 ∶ 2

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In a triangle ABC, a line is drawn from C which bisects AB at point D. Find the ratio of the area of triangles DBC and ABC.a)1 ∶ 1b)2 ∶ 1c)1 ∶ 2d)1 ∶ 3Correct answer is option 'C'. Can you explain this answer?

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