The sides of a right-angled triangle are in arithmetic progression. If the triangle has area 96 sq.units then length of its smallest side is $K$ then $\frac{K}{4} =____$

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answer is 3.

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Detailed Solution

Let sides are
$a - d, a, a + b \Rightarrow a^{2} + {(a - d)}^{2} = {(a + d)}^{2} \Rightarrow a = 4 d$
sides are $3 d, 4 d, 5 d$
Area $= 96$ $\frac{1}{2} \times 3 d \times 4 d = 96$ $\Rightarrow d = 4$
Smallest side $= 12$

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