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
Answers
Answer:
Refer to the attachment
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
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→ area = 3 × 4√15
→ area = 12√15
Hence, perimeter of an equilateral triangle = 12√15 .