Triangle Construction

This is a problem a friend gave me a few months back. Here goes:-

"Construct an equilateral triangle with area equal to the area of any given triangle using only straight-edge and compass."

I was wondering where to start from, which approach to use. I already tried the inradius, semi-perimeter and area relation. That reduced it to constructing an equilateral triangle with side length = Perimeter and Height = inradius of the given triangle.

But this seems harder to do than the original!

#Geometry

Easy Math Editor

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Comments

Nice, ill try

Mahdi Raza - 1 year ago

Did you try the approach in which you construct a parallelogram on two of the triangle's sides?

Sachetan Debray - 1 year 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}`	$\boxed{123}$