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05/01/2022 1:19 pm
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A wire of length 20 is cut into two parts one is made into a regular hexagon of side a and the other to square. Find 'a' if the combined area of a square and regular hexagon is minimum.
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05/01/2022 1:24 pm
4b + 6a = 20
⇒ b = \(\frac{20 -6a}{4}\) = \(5 - \frac{3}{2}a\)
A = \(b^2 + \frac{3\sqrt 3 a^2}{2}\)
A = \(5 - (\frac{3}{2}a)^2\) + \(\frac{3\sqrt 3 a^2}{2}\)
\(\frac{dA}{db}\) = 3√3a - \(\frac{3}{2}\) x 2(5 – \(\frac{3a}{2}\)) = 0
⇒ 3√3 a + \(\frac{9}{2}a\) = 15
⇒ 2√3 a + 3a =10
⇒ a = \(\frac{10}{2\sqrt 3}\)