Question

In Fig. 1, DE || BC, AD = 1 cm and BD = 2 cm. What is the ratio of the ar traingle ABC to the ar traingle ADE ?​

Answer 1

Given:

$\implies$ AD = 1 cm

$\implies$ BD = 2 cm

$\implies$ DE || BC

In ∆ADE and ∆ABC,

$\implies$ ∠ADE = ∠ABC (Corresponding angles)

$\implies$ ∠A = ∠A [Common]

Therefore:

By A.A. similar condition: ∆ADE ~ ∆ABC

We know that:

Ratio of areas of similar triangle is equal to the square of the ratio of the corresponding sides.

Therefore:

$\implies$ $\frac{ar \: \triangle ABC}{ar \: \triangle ADE} = \frac{ {AB}^{2} }{ {AD}^{2} }$

$\implies$ $\frac{ar \: \triangle ABC}{ar \: \triangle ADE} = (\frac{3}{1}) ^{2}$

$\implies$ $\frac{ar \: \triangle ABC}{ar \: \triangle ADE} = \frac{9}{1}$

Final answer: 9:1

Answer 2

Step-by-step explanation:

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