Question

ar ∆ABC, DE || BC. If DE = 3 cm, BC = 6 cm, and ar(A ADE) = 15 cm?, Find the area of ∆ ABC​

Answer 1

DE || BC

DE = 3 cm,

BC = 6 cm area

(∆ADE) = 15 cm2

Now, In ∆ABC

DE ||BC. Therefore triangles, ∆ADE and ∆ABC are similar

$\frac{area \: of \: (traingle \: ade)}{area \: of \: (traingle \: abc)} = \frac{de {}^{2} }{bc {}^{2} }$

$\frac{15}{area \: of \: traingle \: abc} = \frac{(3) {}^{2} }{(6) {}^{2} } = \frac{9}{36}$

$area \: of \: traingle \: abc = \frac{15 \times 36}{9} = 60$

Area of traingle ABC=60cm^2

Answer 2

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