D and E are points on the sides AB and AC respectively of triangle ABC such that AD = 3 cm, BD = 3 cm, BC = 7.5 cm and DE ॥ BC. Then the length of DE (in cm) is:

Question

Question

This question was previously asked in

Bihar STET TGT (Maths) Official Paper-I (Held On: 04 Sept, 2023 Shift 1)

Answer 1

Given:

DE ॥ BC

AD = 3 cm

BD = 3 cm

BC = 7.5 CM

Calculation:

F1 Teaching Arbaz 24-1-24 D5

In ΔABC and ΔADE

∠ADE = ∠ABC (Corresponding angles)

∠AED = ∠ACB (Corresponding angles)

So ΔABC and ΔADE are similar by AA property

AD/DE = AB/BC

⇒ 3/DE = 6/7.5

⇒ DE = 3.75