Question

Find the area of the triangle whose isdes are 42 cm, 34 cm and 20 cm in length. Hence, find the height corresponding to the 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