Properties of triangles

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Question

If the radius of the in circle of a triangle with its sides $5 k,$ $6 k,$ and $5 k$ is 6, then $k$ is equal to

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Solution

We have,
${\begin{array}{l} s = 8 k and, Δ = \sqrt{8 k \times 3 k \times 2 k \times 3 k} = 12 k^{2} \\ ∴ r = \frac{Δ}{s} \Rightarrow \frac{12 k^{2}}{8 k} = 6 \Rightarrow k = 4 . \end{array}}_{}$

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