Question

the side of triangle are 6cm 8cm and 10cm respectively then find the smallest altitude


I will mark brainlist for only correct answer ​

Answer 1

the smallest altitude of side of triangle is 6CM

Answer 2

Given:

✰ The sides of triangle are 6 cm, 8 cm and 10 cm respectively.

To find:

✠ The length of its smallest altitude.

Solution:

We will first find out the area of a triangle using Heron's formula. As we are provided with the three sides of the triangle, putting the values in the formula and then doing the required calculations, we will find the area of a triangle.

Let's find out...✧

➛ Semi-perimeter ( S ) = (6 + 8 + 10)/2

➛ Semi-perimeter ( S ) = 24/2

➛ Semi-perimeter ( S ) = 12 cm

✭ Area of triangle = √s( s - a ) ( s - b ) ( s - c ) ✭

Where,

• a, b and c are the three sides of triangle respectively.

Putting the values in the formula, we have:

➛ Area of triangle = √12( 12 - 6 ) ( 12 - 8 ) ( 12 - 10 )

➛ Area of triangle = √(12 × 6 × 4 × 2)

➛ Area of triangle = √576

➛ Area of triangle = 24 cm²

Now, find out the length of its smallest altitude.

✭ Area = 1/2 × b × h ✭

Here,

• b is the length of its base.
• h is the corresponding height or the smallest altitude of a triangle.

Putting the values in the formula, we have:

➤ 24 = 1/2 × 6 × h

➤ 24 = 3 × h

➤ h = 24/3

➤ h = 8 cm

∴ The length of its smallest altitude = 8 cm

_______________________________