In ΔABC, P and Q are points on sides AB and AC respectively and PQ

1.	In ΔABC, P and Q are points on sides AB and AC respectively and PQ \|\| BC. If length of sides AP, AB and PQ are 5 cm,15 cm and 10 cm respectively, find the length of side BC? 1. 20 cm2. 3 cm3. 15 cm4. 30 cm
Answer» Correct Answer - Option 4 : 30 cm Given: In ΔABC, PQ \|\| BC. AP = 5 cm, AB = 15 cm and PQ = 10 cm Concepts used: Rule of similarity - AA, that is Angle-angle. If two triangles are similar, the ratio of corresponding sides is equal. Calculation: In ΔAPQ and ΔABC, ∠APQ = ∠ABC (Correspnding angles are equal when PQ \|\| BC) ∠PAQ = ∠BAC (Common angle) ∴ ΔAPQ ∼ ΔABC (By AA). As ΔAPQ ∼ ΔABC, ⇒ AP/AB = PQ/BC (Ratio of corresponding sides of similar triangles is equal) ⇒ 5/15 = 10/BC ⇒ 1/3 = 10/BC ⇒ BC = 3 × 10 ⇒ BC = 30 cm. ∴ The length of side BC is 30 cm.

In ΔABC, P and Q are points on sides AB and AC respectively and PQ || BC. If length of sides AP, AB and PQ are 5 cm,15 cm and 10 cm respectively, find the length of side BC? 1. 20 cm2. 3 cm3. 15 cm4. 30 cm

Answer» Correct Answer - Option 4 : 30 cm

Given:

In ΔABC, PQ || BC.

AP = 5 cm, AB = 15 cm and PQ = 10 cm

Concepts used:

Rule of similarity - AA, that is Angle-angle.

If two triangles are similar, the ratio of corresponding sides is equal.

Calculation:

In ΔAPQ and ΔABC,

∠APQ = ∠ABC (Correspnding angles are equal when PQ || BC)

∠PAQ = ∠BAC (Common angle)

∴ ΔAPQ ∼ ΔABC (By AA).

As ΔAPQ ∼ ΔABC,

⇒ AP/AB = PQ/BC (Ratio of corresponding sides of similar triangles is equal)

⇒ 5/15 = 10/BC

⇒ 1/3 = 10/BC

⇒ BC = 3 × 10

⇒ BC = 30 cm.

∴ The length of side BC is 30 cm.