Question: Areas of Triangles and Circles

Comment on Areas of Triangles and Circles

I think that an unknown number cannot be divided and multified because we don't know whether the number is negative or positive. However, this explanation above the video tells us to devide the unkown number. In this point, I am curious how can the unknown number can be divided? Maybe is it because the unknown number is square?
greenlight-admin's picture

You are partly correct; when using the Matching Operations strategy ( 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 when you calculate Quantity A using A=(1/2)bh and determine height using the 30-60-90 ratio of sides? I tried but am getting a different answer.
greenlight-admin's picture

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:

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?

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