lf $Δ$ is the area of triangle whose sides are a,b,c then the area of the triangle with $2 a, 2 b, 2 c$ as the sides is

2 Δ

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4 Δ

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8 Δ

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16 Δ

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Solution

The correct option is B $4 Δ$
$Δ = \sqrt{s (s - a) (s - b) (s - c)}$
$Δ = \sqrt{(\frac{a + b + c}{2}) (\frac{a + b - c}{2}) (\frac{b + c - a}{2}) (\frac{a + c - b}{2})}$
$Δ^{1} = \sqrt{(\frac{2 a + 2 b + 2 c}{2}) (\frac{2 a + 2 b - 2 c}{2}) (\frac{2 b + 2 c - 2 a}{2}) (\frac{2 a + 2 c - 2 b}{2})}$
$Δ^{1} = 4 \sqrt{(\frac{a + b + c}{2}) (\frac{a + b - c}{2}) (\frac{b + c - a}{2}) (\frac{a + c - b}{2})}$
$Δ^{1} = 4 Δ$

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