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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
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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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