If 3 sides of a triangle are 6 cm, 8 cm, and 10 cm, then the altitude of the triangle, using the largest side as its base, will be -
Solution
Correct Answer: Option A
Semi perimeter of the triangle is, S = (6 + 8 + 10)/2
= 12 cm
Area of the triangle is = √{s(s - a)(s - b)(s - c)}
= √{12(12 - 6) (12 - 8) (12 - 10)
= √(12 × 6 × 4 × 2)
= √576
= 24 sq. cm
Area of the triangle = (1/2) × base x height
⇒ 24 = (1/2) × b × h
⇒ b × h = 48
⇒ h = 48/b
⇒ h = 48/10
∴ h = 4.8 cm
= 12 cm
Area of the triangle is = √{s(s - a)(s - b)(s - c)}
= √{12(12 - 6) (12 - 8) (12 - 10)
= √(12 × 6 × 4 × 2)
= √576
= 24 sq. cm
Area of the triangle = (1/2) × base x height
⇒ 24 = (1/2) × b × h
⇒ b × h = 48
⇒ h = 48/b
⇒ h = 48/10
∴ h = 4.8 cm
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