Given: Side 1 = a (let) = 42 cm

Side 2 = b (let) = 34 cm

Side 3 = c (let) = 20 cm

We know that,

Area of a scalene triangle = √(s(s-a) (s-b) (s-c))

Where,

⇒ s = 48 cm

Now,

Area of a scalene triangle = √(48cm × (48-42)cm × (48-34)cm × (48-20)cm)

= √(48cm × 6cm × 14cm × 28cm)

= √112896 cm²

= 336 cm²

Clearly,

Length of longest side = 42 cm

Now,

We know that,

Area of a triangle = 1/2 × Base × Height

⇒ 336 cm² = 1/2 × 42 cm × Height

⇒ 336 cm² = 21 cm × Height

⇒ Height = 16 cm