Question

The sides of triangle are 61 cm, 54 cm and 35 cm respectively. The length of its longest altitude is: 

1. 10 √5 cm 

2. 16 √5 cm 

3. 24 √5 cm 

4. 28 √5 cm

Answer 1

3. 24 √5 cm 

Longest altitude corresponds to shortest side = h₃₅ 

s = 75

Δ = \(\sqrt{(75)(14)(21)(40)}\)

= \(\sqrt{25\times3\times2\times7\times7\times3\times4\times5\times2}\)

= \(420\sqrt{5}\)

∴ \(\frac{1}{2}\) x 35 x h₃₅ = \(420\sqrt{5}\)

h₃₅ = \(24\sqrt{5}\)