Question

Find the area of the triangle whose sides are 42cm 34cm and 20cm find the height corresponding to longest side

Answer 1

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 .

HOPE IT HELPS....