Question

In the given figure, DE || BС. If AD : AB = 1 : 3 and AE = 2.5 cm, then AC equals

Options

• 7.5 cm

• 5 cm

• 10 cm

• 2.5 cm

Answer 1

7.5 cm

Explanation:

Given:

In ΔABC, DE || BC

AD : AB = 1 : 3

AE = 2.5 cm

To find:

Length of AC

Calculation:

In ΔADE and ΔABC:

∠A = ∠A   ...(Common)

∠ADE = ∠ABC   ...(Corresponding angles as DE || BC)

By AA similarity criterion:

ΔADE ∼ ΔABC

Since corresponding sides of similar triangles are proportional:

`(AD)/(AB) = (AE)/(AC)`

Substituting the given values:

`1/3 = 2.5/(AC)`

AC = 2.5 × 3

AC = 7.5 cm