Question

Triangle ABC,DE paralal To BC, AD/DB=3/4,If BC/DE=?​

Answer 1

Given:

In ΔABC,

DE // BC

$\frac{AD}{DB} = \frac{3}{4}$

To find:

$\frac{BC}{DE}$

Solution:

In Δ ADE and ΔABC, we have

∠A = ∠A ....... [common angle]

∠ADE = ABC ....... [corresponding angles since DE // BC (given)]

∴ Δ ADE ~ ΔABC ..... [by AA Similarity]

We know that the corresponding sides of two similar triangles are proportional to each other.

∴ $\frac{AD}{AB} = \frac{DE}{BC}$

⇒ $\frac{AD}{AD \:+\: DB} = \frac{DE}{BC}$

substituting AD = 3 and DB = 4

⇒ $\frac{3}{3 \:+\: 4} = \frac{DE}{BC}$

⇒ $\frac{3}{7} = \frac{DE}{BC}$

⇒ $\bold{\frac{BC}{DE} = \frac{7}{3}}$

Thus, the final answer is $\underline{\bold{\frac{BC}{DE} = \frac{7}{3}}}.$

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Answer 2

Step-by-step explanation:

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