Question

A copper wire is bent in the form of an equilateral triangle of area 4√ 3 cm² .If the same wire is bent into the form of a square, the area of the square will be:
1. 16 sq.cm
2. 9 sq.cm
3. 144 sq.cm
4. 64 sq.cm

Answer 1

Correct Answer - Option 2 : 9 sq.cm

Given:

Equilateral triangle area = 4√3 cm²

Formula used:

if side of an equilateral is a 

Perimeter of equilateral traingle = 3 × a 

Area of equilateral triangle = (√3/4) × a²

if side of square is b

Perimeter of square = 4 × b

Area of square = b²

Calculation:

Equilateral triangle area = 4√3 cm2 

⇒ (√3/4) × a² = 4√3

⇒ a² = 4√3/(√3/4)

 ⇒ a2 = 16

⇒ a = √16

⇒ a = 4 cm 

∴ Perimeter of equilateral traingle = 3 × 4

⇒ Perimeter of equilateral traingle = 12 cm

According to question perimeter of square is equal to perimeter of triangle

∴ Perimeter of square = 4 × b

⇒ 12 = 4 × b

⇒ b = 12/4

⇒ b = 3 cm

Area of a square = 3²

⇒ Area of a square = 9 cm²

∴ area of square is 9 cm².