If every side of an equilateral triangle is doubled, the area of the new triangle is $k$ times the area of the old one. So, $k$ is equal to

\sqrt{2}

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2

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3

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4

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Solution

The correct option is A $4$
Let $A_{1}$ be the area of the original equilateral triangle and $A_{2}$ be the area of the new one.
$A_{1} = \frac{\sqrt{3}}{4} a^{2}$
$A_{2} = \frac{\sqrt{3}}{4} {(2 a)}^{2} = 4 \times \frac{\sqrt{3}}{4} a^{2}$
Hence, $A_{2} = 4 A_{1}$
$∴ k = 4$

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