A wire when bent in the form of an equilateral triangle encloses an area of 64 -3 cm 2- The area enclosed by the same wire when bent to form a square is cm 2A- 81B- 100C- 144D- 16

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A wire when b...

Question

A wire when bent in the form of an equilateral triangle encloses an area of $64 \sqrt{3} c m^{2} .$ The area enclosed by the same wire when bent to form a square is ___ $c m^{2}$

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100

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144

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Solution

The correct option is D
144

Let the side of the equilateral $Δ l e$ 'a' and the side of the square be 'x' we know, area of equilateral $Δ = \frac{\sqrt{3}}{4} a^{2}$

$64 \sqrt{3} = \frac{\sqrt{3}}{4} a^{2}$

$∴ a^{2} = 8^{2} \times 2^{2}$

$a = 16 c m$

Perimeter of equilateral $Δ = 3 (16)$

= 48 cm

Hence, perimeter of square = 48 cm

i.e., $4 \times = 48 \Rightarrow x = 12 c m$

Area of square $= x^{2}$

$= (12)^{2}$

$= 144$

Hence (D)

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A wire when bent in the form of an equilateral triangle encloses an area of 64√3 cm2. The area enclosed by the same wire when bent to form a square is ___ cm2

A wire when bent in the form of an equilateral triangle encloses an area of $64 \sqrt{3} c m^{2} .$ The area enclosed by the same wire when bent to form a square is ___ $c m^{2}$