Is there a way to cut up an equilateral triangle and reorganize the parts to get a square of the same surface area?

Guest Mar 25, 2015

#1**+5 **

Well there is of course but working out the best cuts would take more time than i have right now.

If you let the side lengths of the equilateral triangle be 2 units then the height will be $$\sqrt3$$ units.

You can multiply these by any constant if you want different side lengths.

The area of the triangle will be $$A=(1/2)*b*h = 0.5*2*\sqrt3 = \sqrt3$$

The are of a square is $$l*l$$ so

$$\\l*l=\sqrt3\\

l^2=3^{1/2}\\

l=3^{1/4}\qquad$or if you prefer $ l=\sqrt[4]{3}\;\; units$$

so if the side of the triangle is 2k units then the side of the square will be $$\sqrt[4]{3}\times k\;\; units$$

Melody
Mar 26, 2015