Question

Find the area of a triangle whose sides are 20 cm, 34 cm and 42 cm. Hence find the height corresponding to the side 42 cm.

Answer 1

Given: The side lengths are 20 cm, 34 cm and 42 cm.

Step-wise calculation:

1. Semi-perimeter:

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

= `96/2`

= 48

2. Area by Heron’s formula: 

Area = `sqrt(s(s - a)(s - b)(s - c))`

= `sqrt(48(48 - 20)(48 - 34)(48 - 42))`

= `sqrt(48 xx 28 xx 14 xx 6)`

Compute factors: 48 × 28 = 1344 and 14 × 6 = 84.

So, product = 1344 × 84 = 16 × 84².

Therefore, Area = `sqrt(16 xx 84^2)`

= 4 × 84

= 336 cm²

3. Height corresponding to side 42 cm:

Area = `1/2` × base 42 × height h 

⇒ 336 = `1/2 xx 42 xx h` 

= 21 × h 

Hence, h = `336/21`

= 16 cm

Area = 336 cm².

Height corresponding to the side 42 cm = 16 cm.