Question

In the given figure, DE || BC. If AC = 20 cm, EC = 5 cm and DE = 12
cm, then BC is equal to
a 15 cm
b 16 cm c)18 cm d) 24. please guys give me answer please ​

Answer 1

Step-by-step explanation:

please give me answer please

Answer 2

Given:

In the given figure, DE || BC. If AC = 20 cm, EC = 5 cm and DE = 12 cm, then BC is equal to?

To find:

The length of BC

Solution:

In Δ ADE and Δ ABC, we get

∠ADE = ∠ABC . . . [corresponding angles]

∠DAE = ∠BAC . . . [common angles]

∴ Δ ADE ~ Δ ABC . . . [By AA similarity]

We know that,

The corresponding sides of two similar triangles are proportional to each other.

Here we have Δ ADE ~ Δ ABC,

∴ $\frac{AE}{AC} = \frac{DE}{BC}$

$\implies \frac{AC - EC}{AC} = \frac{DE}{BC}$

on substituting AC = 20 cm, EC = 5 cm and DE = 12 cm

$\implies \frac{20 - 5}{20} = \frac{12}{BC}$

$\implies \frac{15}{20} = \frac{12}{BC}$

$\implies \frac{3}{4} = \frac{12}{BC}$

$\implies BC = 4 \times 4$

$\implies \bold{BC = 16\:cm}$ ← option (b)

Thus, the length of BC is → 16 cm.

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Also View:

In figure.6.17. (i) and (ii), DE || BC. Find EC in (i) and AD in (ii). (i) (ii)

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In the given figure. If DE|| BC Find EC.​

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