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 cm
2. 30 cm
3. 10 cm
4. None of the above
1. 15 cm
2. 30 cm
3. 10 cm
4. None of the above
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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.