Question

Find the area of the triangle with sides 21 cm, 16 cm and 13 cm. Also, find the perimeter of an equilateral
triangle equal in area to this triangle.​

Answer 1

Answer :-

Refer to the attachment

Answer 2

GIVEN :

The area of the triangle with sides 21cm, 16cm and 13cm are given respectively.

TO FIND :

The perimeter of an equilateral triangle is equal in area to this triangle = ?

STEP-BY-STEP EXPLANATION :

Now, we will find the perimeter of an equilateral triangle here –

Formula used :

→ Area of the triangle (heron's formula)

→ Side = a + b + c/2

[ substituting the values as per formula ] :

→ Side = 21 + 16 + 13 / 2

→ side = 50/2 [ When reduced] = 25

→ area = √s (s-a) × (s-b) × (s-c)

→ area = √25 (25-21) × (25-16) × (25-13)

→ area = √25 × 4 × 9 × 12

→ area = √5 × 5 × 2 × 2 × 3 × 3 × 2 × 3 × 2

→ area = 60√3

Now, we got here area = 60√3 .

Therefore, perimeter of an equilateral triangle = ?

→ perimeter = √3/4 (a²)

→ 60√3 = √3/4 (a²)

→ 60 = (a²)/4

→ a² = 4 × 60

→ a = √240

→ a = 4√15

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

→ area = 3 × 4√15

→ area = 12√15

Hence, perimeter of an equilateral triangle = 12√15 .