If the radius of the incircle of a triangle with its sides $5 k, 6 k, 5 k$ is $6$ , then $k$ is equal to?

3

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4

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5

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6

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Solution

The correct option is B $4$
We know, $s = \frac{a + b + c}{2}$
$s = \frac{5 k + 6 k + 5 k}{2}$
$∴ s = 8 k$
$Δ = \sqrt{8 k \times 3 k \times 3 k \times 2 k} = 12 k^{2}$
$\Rightarrow r = \frac{Δ}{s}$
$6 = \frac{12 k^{2}}{8 k}$
$∴ k = 4$

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