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Suppose the altitudes of a triangle are \(10,12,15\), what is its semi-perimeter?

Note by Vilakshan Gupta 2 months ago

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@Tapas Mazumdar did u also give prmo

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No. Was the above problem asked in that?

yup

@Vilakshan Gupta – The answer I'm getting is \(\dfrac{60}{\sqrt 7}\), is that correct? What was your method?

@Tapas Mazumdar – Correct. I left it because i didn't get an integer. The question is bonused

If the altitudes of a triangle are \(h_1\), \(h_2\) and \(h_3\) respectively and let \(2 \mathbb{H} = \dfrac{1}{h_1} + \dfrac{1}{h_2} + \dfrac{1}{h_3}\), then

\[4 s^2 = \dfrac{\mathbb{H}}{ \left( \mathbb{H} - \frac{1}{h_1} \right) \left( \mathbb{H} - \frac{1}{h_2} \right) \left( \mathbb{H} - \frac{1}{h_3} \right) } \]

Bonus!

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TopNewest@Tapas Mazumdar did u also give prmo

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No. Was the above problem asked in that?

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yup

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If the altitudes of a triangle are \(h_1\), \(h_2\) and \(h_3\) respectively and let \(2 \mathbb{H} = \dfrac{1}{h_1} + \dfrac{1}{h_2} + \dfrac{1}{h_3}\), then

\[4 s^2 = \dfrac{\mathbb{H}}{ \left( \mathbb{H} - \frac{1}{h_1} \right) \left( \mathbb{H} - \frac{1}{h_2} \right) \left( \mathbb{H} - \frac{1}{h_3} \right) } \]

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Bonus!

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