Question

If the sides of a triangle are 4 cm, 6 cm and 6 cm, then find the height corresponding to the smallest side.

Answer 1

Answer:4√2cm

Step-by-step explaination:

Let the triangle be ∆ABC. Let the height be AD.

Where,

AB=AC=6cm

BD=DC=2cm

By using Pythagoras theorem,

In∆ADB,

AB^2=AD^2+DB^2

AB^2-DB^2=AD^2

(6)^2-(2)^2. =AD^2

36-4.=AD^2

AD^2= 32

AD=4√2cm

Answer 2

The height of the triangle will be 4√2 cm

Step-by-step explanation:

Given:

sides of triangle = a=4cm,b= 6cm, c=6cm

To find:

height corresponding to the lower side (a)=4cm

Solution:

First, we find the area of the triangle given

For that, we will need the semi-perimeter(s)

s= a+b+c  

      2

s= 4+6+6

       2

s=16/2

s=8

Now, Area of the given traingle= √s(s-a) (s-b) (s-c)

Area of the traingle= $\sqrt{8 (8-4) (8-6) (8-6)$

∴ Area of traingle= $\sqrt{8 (4) (2) (2)$

∴ Area of traingle= $\sqrt{ 8 (16)$

∴ Area of traingle= √128

∴ Area of traingle= 8√2 sq cm.

So we find the height using this area given

The base will be counted as 4 because that is the condition given

∴ Area of traingle= 1/2 x base x height

∴ Area of traingle= 1/2 x 4 x height

8 √2= 1/2 x 4 x height

8 √2= 2 x height

∴ 8√2  = height

   2

∴ height = 4√2 cm

The height corresponding to the smallest side is 4√2 cm

#SPJ3