Question

Find the area of the triangle whose sides are 42 cm, 34 cm, and 20 cm in length. hence, find the height corresponding to the longest side??

Answer 1

Hi ,

Let the side of the triangle are

a = 42 cm

b = 34 cm

c = 20 cm

We know that,
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By Heron's formula :


Area of the triangle ( A )

A = √ s ( s - a ) ( s - b ) ( s - c )

Where s = ( a + b + c ) / 2

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s = ( 42 + 34 + 20 ) / 2

s = 96 / 2

s = 48

s - a = 48 - 42 = 6

s - b = 48 - 34 = 14

s - c = 48 - 20 = 28

Therefore ,

A = √ s ( s - a ) ( s - b ) ( s - c )

A = √ 48 × 6 × 14 × 28

A = √ 4 × 4 × 3 ×7 × 2× 7× 2 × 2

A = √( 4 × 4 )×( 7 × 7 )×( 2×2 )×3×2

A = 4 × 7 × 2 √6

A = 56√6 square cm -----( 1 )

ii ) long side = a = 42 cm

Let the corresponding height = h cm

A = ah /2

56√6 = ( 42 × h ) / 2 [ from ( 1 )]

( 56√6 × 2 ) / 42 = h

After cancellation , we get

8√6/3 = h

Therefore ,

Corresponding height to the

longest side = h = 8√6 / 2 cm

I hope this helps you.

:)