If the semi-perimeter of ΔABC with sides AB and AC is 8 cm and 12 cm

1.	If the semi-perimeter of ΔABC with sides AB and AC is 8 cm and 12 cm respectively is 15 cm, find the length of side BC.1. 15 cm2. 30 cm3. 10 cm4. None of the above
Answer» Correct Answer - Option 3 : 10 cm Given: In ΔABC, AB = 8 cm and AC = 12 cm. Semi-perimeter of ΔABC = 15 cm Concepts used: Semi-perimeter of triangle = Sum of three sides of a triangle/2 Calculation: Semi-perimeter of triangle = Sum of three sides of a triangle/2 ⇒ Semi-perimeter of ΔABC = (AB + BC + AC)/2 ⇒ Semi-perimeter of ΔABC = (8 + BC + 12) cm/2 ⇒ 15 cm = (20 + BC) cm/2 ⇒ 15 cm × 2 = 20 cm + BC ⇒ BC = 30 cm – 20 cm ⇒ BC = 10 cm. ∴ The length of side BC is 10 cm.

If the semi-perimeter of ΔABC with sides AB and AC is 8 cm and 12 cm respectively is 15 cm, find the length of side BC.1. 15 cm2. 30 cm3. 10 cm4. None of the above

Answer» Correct Answer - Option 3 : 10 cm

Given:

In ΔABC, AB = 8 cm and AC = 12 cm.

Semi-perimeter of ΔABC = 15 cm

Concepts used:

Semi-perimeter of triangle = Sum of three sides of a triangle/2

Calculation:

Semi-perimeter of triangle = Sum of three sides of a triangle/2

⇒ Semi-perimeter of ΔABC = (AB + BC + AC)/2

⇒ Semi-perimeter of ΔABC = (8 + BC + 12) cm/2

⇒ 15 cm = (20 + BC) cm/2

⇒ 15 cm × 2 = 20 cm + BC

⇒ BC = 30 cm – 20 cm

⇒ BC = 10 cm.

∴ The length of side BC is 10 cm.

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