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## Comment on

Areas of Triangles and Circles## I think that an unknown

## You are partly correct; when

You are partly correct; when using the Matching Operations strategy (https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...) for Quantitative Comparison questions, we cannot divide by a variable if we aren't sure whether the variable is positive or negative.

However, in this case, the variable represents a length, and lengths are always positive.

Also note that we are dividing both quantities by k², and k² can never be negative.

For those two reasons, we can safely both quantities by k²

## Can you show how to solve

## It'll save you a lot of time

It'll save you a lot of time if you memorize the formula for the area of an equilateral triangle.

That said, here's how you'd find the triangle's height using a 30-60-90 special triangle: https://imgur.com/WeDdLIC

You'll see that the right triangle has a hypotenuse of length 4k, and the side opposite the 30° has length 2k.

So, we can find the length of the third side (aka the height) using the Pythagorean theorem or by applying what we know about 30-60-90 special right triangles.

Either way, it turns out the third side has length (2√3)k

Does that help?