If the radius of incircle of ΔABC is √2 cm and the length of sides

1.	If the radius of incircle of ΔABC is √2 cm and the length of sides AB, BC and AC is 5 cm, 6 cm and 9 cm respectively, what is the area of ΔABC?1. 20√2 cm22. 10√2 cm23. 15 cm24. 10.4 cm2
Answer» Correct Answer - Option 2 : 10√2 cm² Given: Radius of incircle (r) = √2 cm AB = 5 cm, BC = 6 cm, AC = 9 cm. Concepts used: Area of ΔABC = 1/2 × r × (AB + BC + AC) Let the length of sides of triangle AB, BC and AC be a, b and c respectively. Using heron's formula - s = (a + b + c)/2 Area of ΔABC = √s(s – a)(s – b)(s – c) Calculation: Using heron's formula - s = (5 + 6 + 9)/2 = 10 cm Area of ΔABC = √s(s – a)(s – b)(s – c) ⇒ √10 × (10 – 5) × (10 – 6) × (10 – 9) cm² ⇒ √(10 × 5 × 4 × 1) cm² ⇒ √200 cm² ⇒ 10√2 cm² ∴ The area of ΔABC is 10√2 cm2. Short trick: Area of ΔABC = 1/2 × r × (AB + BC + AC) cm2 ⇒ 1/2 × √2 × (5 + 6 + 9) cm² ⇒ 1/2 × √2 × 20 cm² ⇒ 10√2 cm² ∴ The area of ΔABC is 10√2 cm².

If the radius of incircle of ΔABC is √2 cm and the length of sides AB, BC and AC is 5 cm, 6 cm and 9 cm respectively, what is the area of ΔABC?1. 20√2 cm22. 10√2 cm23. 15 cm24. 10.4 cm2

Answer» Correct Answer - Option 2 : 10√2 cm²

Given:

Radius of incircle (r) = √2 cm

AB = 5 cm, BC = 6 cm, AC = 9 cm.

Concepts used:

Area of ΔABC = 1/2 × r × (AB + BC + AC)

Let the length of sides of triangle AB, BC and AC be a, b and c respectively.

Using heron's formula -

s = (a + b + c)/2

Area of ΔABC = √s(s – a)(s – b)(s – c)

Calculation:

Using heron's formula -

s = (5 + 6 + 9)/2 = 10 cm

Area of ΔABC = √s(s – a)(s – b)(s – c)

⇒ √10 × (10 – 5) × (10 – 6) × (10 – 9) cm²

⇒ √(10 × 5 × 4 × 1) cm²

⇒ √200 cm²

⇒ 10√2 cm²

∴ The area of ΔABC is 10√2 cm2.

Short trick:

Area of ΔABC = 1/2 × r × (AB + BC + AC) cm2

⇒ 1/2 × √2 × (5 + 6 + 9) cm²

⇒ 1/2 × √2 × 20 cm²

⇒ 10√2 cm²

∴ The area of ΔABC is 10√2 cm².