Post your question in the Comment section below, and a GRE expert will answer it as fast as humanly possible.
- Video Course
- Video Course Overview
- General GRE Info and Strategies - 7 videos (free)
- Quantitative Comparison - 7 videos (free)
- Arithmetic - 42 videos
- Powers and Roots - 43 videos
- Algebra and Equation Solving - 78 videos
- Word Problems - 54 videos
- Geometry - 48 videos
- Integer Properties - 34 videos
- Statistics - 28 videos
- Counting - 27 videos
- Probability - 25 videos
- Data Interpretation - 24 videos
- Analytical Writing - 9 videos (free)
- Sentence Equivalence - 39 videos (free)
- Text Completion - 51 videos
- Reading Comprehension - 16 videos
- Study Guide
- Philosophy
- Office Hours
- Extras
- Prices
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?