Question

In adjoining figure in D ABC, point D is on side AC. If AC = 16, DC = 9 and

BP | AC, then find the following ratios.

(i) A( ∆ ABD) / A( ∆ ABC) (ii) A( ∆ BDC) / A( ∆ ABC) (iii) A( ∆ ABD) / A( ∆ BDC)​

Answer 1

Given :- adjoining figure in D ABC, point D is on side AC. If AC = 16, DC = 9 and BP ⟂AC, then find the following ratios :-

(i) A(∆ABD) / A( ∆ABC)

(ii) A(∆BDC) / A( ∆ABC)

(iii) A(∆ABD) / A(∆BDC)

Solution :-

we know that,

• Area of ∆ = (1/2) * Base * perpendicular height .

so,

→ A(∆ABD) / A( ∆ABC) = (1/2) * AD * BP / (1/2) * AC * BP = AD/AC = (AC - DC)/AC = (16 - 9)/16 = (7/16) (i)

and,

→ A(∆BDC) / A( ∆ABC) = (1/2) * DC * BP / (1/2) * AC * BP = DC/AC = (9/16) (ii)

also,

→ A(∆ABD) / A(∆BDC) = (1/2) * AD * BP / (1/2) * DC * BP = AD/DC = (AC - DC)/DC = (16 - 9)/9 = (7/9) (iii)

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