In ∆ABC, D is a point on side BC such that BC = 5 × BD and A(∆ABC) is 100 sq. units. What is the area of ∆ABD in sq. units?
Explanation:
BC is the base of ∆ABC and BD is base of ∆ABD.
If we drop a perpendicular from A on the line BC, this line is the height for both, ∆ABC and ∆ABD
∴ The ratio of the areas of the two triangles is equal to the ratio of their bases.
∴ A(∆ABD) = 1/5 × A(∆ABC)
∴ A(∆ABD) = 1/5 × 100 = 20 sq. units
Hence, option (a).
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