Correct Answer - Option 2 : 25.8 cm
Given:
Sides of a triangle = 30 cm, 28 cm and 26 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
\(\dfrac{30 \ + \ 28 \ + \ 26}{2}\) = 42
Area of the triangle
= \(\sqrt{42(42 \ - \ 30)(42 \ - \ 28)(42 \ - \ 26)}\)
⇒ \(\sqrt{42\ × \ 12\ × \ 14\ × 16}\) = √112896 = 336 cm2
The largest altitude will be on side 26 cm
336 = 1/2 × 26 × Altitude
⇒ Altitude = 672/26 = 25.8 cm
∴ The longest altitude is 25.8 cm
