Question

Find the area of the triangle whose sides are 42 cm 34cm 20cm in lenth.Hence ,find the height corresponding to the longest side. Hurry up

Answer 1

Perimeter = Sum of all sides

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
then , height =( 336 *2 )/42
= 672 / 42 = 16 cm is the longest side.

Answer 2

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