#17

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

#Geometry

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Comments

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

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

Tapas Mazumdar - 3 years, 9 months ago

Bonus!

Md Zuhair - 3 years, 9 months ago

@Tapas Mazumdar did u also give prmo

Vilakshan Gupta - 3 years, 9 months ago

No. Was the above problem asked in that?

Tapas Mazumdar - 3 years, 9 months ago

yup

Vilakshan Gupta - 3 years, 9 months ago

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

Tapas Mazumdar - 3 years, 9 months ago

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

Vilakshan Gupta - 3 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$