Question

A wire when bent in the form of a square encloses an area of 16 cm². Find the area enclosed by it when the same wire is bent in the form of an equilateral triangle

Answer 1

Let the side of a square = x cm
Its area = 16cm² 
⇒ x² = 16
⇒ x = 4cm
Clearly, the length of the wire
= Perimeter of a square
= 4 x 4
= 16cm² 
Let the side of an equilateral triangle = a cm
Now, the perimeter of an equilateral triangle
= length of the wire
⇒ 3a = 16

⇒ a = `(16)/(3)"cm"`

∴ Area of an equilateral triangle

= `sqrt(3)/(4) xx "a"^2`

= `sqrt(3)/(4) xx (16)/(3) xx (16)/(3)`

= `(64sqrt(3))/(9)"cm"^2`.