If the sides of the triangle are 5K, 6K, 5K a | vedclass

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(A) Let the sides of the triangle be $a = 5K$,$b = 6K$,and $c = 5K$.The semi-perimeter $s$ is given by $s = \frac{a + b + c}{2} = \frac{5K + 6K + 5K}{

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$4$

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(A) Let the sides of the triangle be $a = 5K$,$b = 6K$,and $c = 5K$.The semi-perimeter $s$ is given by $s = \frac{a + b + c}{2} = \frac{5K + 6K + 5K}{2} = \frac{16K}{2} = 8K$.The area of the triangle $\Delta$ using Heron's formula is $\Delta = \sqrt{s(s - a)(s - b)(s - c)}$.Substituting the values: $\Delta = \sqrt{8K(8K - 5K)(8K - 6K)(8K - 5K)} = \sqrt{8K 	imes 3K 	imes 2K 	imes 3K} = \sqrt{144K^4} = 12K^2$.The radius of the incircle $r$ is given by $r = \frac{\Delta}{s}$.Given $r = 6$,we have $6 = \frac{12K^2}{8K}$.Simplifying the expression: $6 = \frac{3K}{2}$.Therefore,$3K = 12$,which gives $K = 4$.

If the sides of the triangle are $5K, 6K, 5K$ and the radius of the incircle is $6$,then the value of $K$ is equal to

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