In triangle ABC AD is median on side BC. Find the length of AD if AB =

1.	In triangle ABC AD is median on side BC. Find the length of AD if AB = 8 cm, BC = 10 cm and AC = 6?1. 5 cm2. 6 cm3. 7 cm4. 8 cm
Answer» Correct Answer - Option 1 : 5 cm Given: In triangle ABC, AD is median on side BC where AB = 8 cm, BC = 10 cm and AC = 6 Concept Used: According to Apollonius theorem the sum of squares of any of the two sides of a triangle equals to twice its square on half of the third side, along with the twice of its square on the median bisecting the third side Calculation: Let ABC is a triangle with AD is median on BC then by Apollonius theorem ∴ (AB² + AC²) = 2 × (BD² + AD²) ∴ ((8)² + (6)²) = 2 × ((5)² + AD²) ⇒ 64 + 36 = 50 + 2 × AD² ⇒ AD² = 25 ⇒ AD = 5 cm Hence, option (1) is correct

In triangle ABC AD is median on side BC. Find the length of AD if AB = 8 cm, BC = 10 cm and AC = 6?1. 5 cm2. 6 cm3. 7 cm4. 8 cm

Answer» Correct Answer - Option 1 : 5 cm

Given:

In triangle ABC, AD is median on side BC where AB = 8 cm, BC = 10 cm and AC = 6

Concept Used:

According to Apollonius theorem the sum of squares of any of the two sides of a triangle equals to twice its square on half of the third side, along with the twice of its square on the median bisecting the third side

Calculation:

Let ABC is a triangle with AD is median on BC then by Apollonius theorem

∴ (AB² + AC²) = 2 × (BD² + AD²)

∴ ((8)² + (6)²) = 2 × ((5)² + AD²)

⇒ 64 + 36 = 50 + 2 × AD²

⇒ AD² = 25

⇒ AD = 5 cm

Hence, option (1) is correct

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