Question

A triangle with sides 42cm 34cm and 20 cm.The biggest side is joint with the the height . Find heigt by heron formula

Answer 1

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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.

Answer 2

SOLUTION

Given,

In ∆ with sides

42cm

34cm

20cm

Side= 42+34+20/2

=) 48cm

√s(s-a)(s-b)(s-c)

=)√48(48-42)(48-34)(48-20)

=)√48× 6× 14× 28

=) √112896

=) 336cm^2