Question

calculate the area of the triangle whose sides are 18 cm 24 cm and 30 cm in length also find the length of the altitude corresponding to the smallest side

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

When three sides are given then we use Heron's formula which is

√[ s( s - a )( s - b )( s - c ) ] where

s = ( a + b + c ) / 2

s = ( 18 + 24 + 30 ) cm / 2

= 72 cm / 2 or 36 cm

√[ 36( 36 - 30 )( 36 - 24 )(36-18)]

√[ 6² × 6 × 2 × 6 × 2 × 3 × 3 ]

= 6 × 6 × 2 × 3 cm² = 216 cm²

Here, longest side = 30 cm

Area of ∆ = 1 / 2 × base × height

216 cm² = 1 / 2 × 30 cm × height

216 cm² × 2 / 30 = height

14.4 cm = height

$\textbf{Hope it helps}$

Have greay future ahead!