= A triangle has sides of lengths 18, 24 and 30 units. What is the length of the shortest altitude of this triangle? Express your answer as a common fraction.

According to the Heron's formula, Area (A) of the triangle having sides a,b,c units is

A=

s(s−a)(s−b)(s−c)

where

s=

2

a+b+c

For the given triangle,

a=18 cm

b=24 cm

c=30 cm

s=

2

18+24+30

=36

A=

36(36−18)(36−24)(36−30)

A=

36×18×12×6

A=

216×216

=216 cm

2

Smallest side =18 cm

Area of the triangle =

2

1

×base×altitude=216

2

1

×18× altitude=216

Altitude =

9

216

=24 cm

Step-by-step explanation:

hope this will help

Here given measure of sides are 18 , 24 and 30 units. Firstly let's find the area of ∆ using Heron's Formula.

Where s is semi Perimeter . And here s will be ( 18 + 24 + 30 ) / 2 = 36 units .

Also we know that ,

Let's find the altitudes now ,

Altitude on side of 18 units :-

Altitude on side of 24 units :-

Altitude on side 30 units :-

step-by-step explanation: