Question

*25. The perimeter of a triangle is 60 cm and the circumference of its incircle is 10πcm. Find the area of the triangle.
plz give step by step explanation​

Answer 1

Given :

• The perimeter of a triangle is 60 cm.

• The circumference of its incircle is 10πcm.

To find :

• The area of the triangle =?

Step-by-step explanation :

As We know that,

Sum of all sides = Perimeter

So,

a + b + c = 60

Now,

We know that,

Circumference of circle = 2πr.

Substituting the values in the above formula, we get,

2πr = 10π

r = 10π/2π

r = 5.

Therefore, Radius of incircle = 5 cm.

Semi - perimeter = a + b + c/2

Substituting the values in the above formula, we get,

= 60/2

= 30.

Therefore, Semi - perimeter = 30 cm.

Now,

Its radius, the inradius (usually denoted by r) is given by r = Δ/S,

Δ is the area of the triangle.

S is the semiperimeter (a+b+c)/2.

So,

r = Δ/S

Δ = S × r

Δ = 5 × 30

Δ = 150.

Therefore, Area of the triangle = 150 cm².

Answer 2

Given: The perimeter of a triangle is 60 cm

The circumference of its incircle is 10

To find : The area of the triangle =?

Step-by-step explanation

As We know that, Sum of all sides = Perimetet So. a + b + c = 60

Now,

We know that, :

2nr 10n t = 10u / 2 * pi r = 5

Therefore,

Radius of inclrcle = 5 cm .

Semt - perimeter = a + b + c / 2 Substituting the values in the above formula, we get.

=60/2 =30

Therefore,

Semi i - perimeter = 30 cm .

Now Its radius,

the inradius (usually denoted by ) is given by r = Delta / S ,

given by r = Delta / S , A is the area of the triangle. S is the semiperimeter (a + b + c) / 2 . So, r = Delta / S triangle=S* r triangle=5*30 triangle=150 . Therefore, Area of the iangle = 150 cm ^ 2