Correct Answer - Option 2 : 11.2 cm
Given:
Sides of a triangle = 13 cm, 14 cm and 15 cm
Formula used:
Area of a triangle = \(√{s(s \ - \ a)(s \ - \ b)(s \ - \ c)}\)
Semiperimeter(s) = \(\dfrac{a \ + \ b \ + \ c}{2}\)
Area of a triangle = 1/2 × Base × Altitude
Calculation:
The semiperimeter of the triangle is
\(\dfrac{13 \ + \ 14 \ + \ 15}{2}\) = 21
Area of the triangle
= \(\sqrt{21(21 \ - \ 13)(21 \ - \ 14)(21 \ - \ 15)}\)
⇒ \(\sqrt{21\ × \ 8\ × \ 7\ × 6}\) = √7056 = 84 cm2
Altitude on the longest side
84 = 1/2 × 15 × Altitude
⇒ Altitude = 168/15 = 11.6 cm
∴ Altitude on the longest side is 11.6 cm.
