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# #17

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

- 1 month, 3 weeks ago

No. Was the above problem asked in that?

- 1 month, 3 weeks ago

yup

- 1 month, 3 weeks ago

The answer I'm getting is $$\dfrac{60}{\sqrt 7}$$, is that correct? What was your method?

- 1 month, 3 weeks ago

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

- 1 month, 3 weeks ago

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

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

- 1 month, 3 weeks ago

Bonus!

- 1 month, 3 weeks ago