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प्रश्न
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
उत्तर
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`.
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