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  1. In figure, DE || BC. If DE = 3 cm, BC = 6 cm and area of ∆ADE = 15 sq. cm, then the area of ∆ABC is

    1. 75 sq. cm.
    2. 45 sq. cm.
    3. 30 sq. cm.
    4. 60 sq. cm.
Correct Option: D


DE || BC
∴ ∠ADE = ∠ABC
∠AED = ∠ACB
By AA–similarity,
∆ADE ~ ∆ABC

Area of ∆ABC
=
BC²
Area of ∆ADEDE²

Area of ∆ABC
=
15

=
36
= 4
9

∴ Area of DABC = 4 × 15
= 60 sq. cm.



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