Answer:

The height corresponding to the longest side is 16 cm.

Step-by-step explanation:

Sides of the triangle are a=42,b=34,c=20

According to Hero's formula,

Area of the triangle, A=

s(s−a)(s−b)(s−c)

Where s=

2

a+b+c

=

2

42+34+20

=48

Now,

A=

48(48−42)(48−34)(48−20)

A=

48(6)(14)(28)

A=

(6×8)(6)(14)(14×2)

A=14×6×4

A=336cm

2

Let the height corresponding to longest side (42cm) is h

Area =

2

1

×base×height

2

1

×42×h=336

h=

42

336×2

=16 cm

Answer:

The height corresponding to the longest side is 16 cm

Step-by-step explanation:

Semiperimeter (s) = (42 + 34 + 20 ) / 2

So it is = 96 / 2 = 48 cm.

Using herons formula = (√s )(√s-a )(√s-b) (√s-c)

By  substituting s and a , b , c   i.e  the given sides.

We have √48 × √6 × √14 × √28

So √ (4 × 6 × 2) × √6 × √(7 × 2) × √(7 × 4)

Simplifying the numbers we have area = 4 × 6 × 2 × 7 = 336 cm ²

Hence area is 336 cm²

Now height corresponding to longest side implies that base is 42 cm and area remains same  

So area of triangle is  1/ 2 b × h

336 = 1/ 2 ×  42 × H

HENCE H = 16 cm

So height is 16 cm .