Question

in triangle ABC, DE parallel to BC, AD:AB = 1:2, BC=6cm​

Answer 1

Step-by-step explanation:

IN Triangle ABC

DE||BC

AD:AB = 1:2

BC =6cm

AD/DB=DE/BC (BY THALSE THEOREM)

1/2=DE/6

2DE=6

DE=3 cm

Answer 2

The length of DE is option (c): 3 cm.

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Complete Question:

In a triangle ABC, DE ‖ BC, if AD : AB = 1 : 2 and BC = 6 cm, then DE is ----

a. 1 cm b. 2 cm c. 3 cm d. 4 cm​

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Let's understand a few concepts:

Let's say we have two triangles Δ ABC and Δ PQR and they are similar to each other, then we can state that their corresponding sides are in the same ratio or are proportional to each other.

$\bigstar\:\boxed{\bold{\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} }}\:\bigstar$

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Let' solve the given problem:

In Δ ABC, we have

DE // BC

AD : AB = 1 : 2 . . . (1)

BC = 6 cm . . . (2)

Let's consider Δ ADE and Δ ABC, we get

∠DAE = ∠BAC . . . [common angles]

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

∴ Δ ADE ~ Δ ABC . . . By AA similarity criteria

From the above, we know that the corresponding sides of the similar triangles ADE and ABC will be proportional to each other.

∴ $\frac{AD}{AB} = \frac{DE}{BC}$

• on substituting from (1) and (2), we get

$\implies \frac{1}{2} = \frac{DE}{6}$

• on multiplying by 6 on both sides

$\implies \frac{1}{2}\times 6 = \frac{DE}{6}\times 6$

$\implies DE = \frac{1}{2}\times 6$

$\implies \bold{DE =3 \:cm}$ ← option (c)

Thus, the length of DE is 3 cm.

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