How To Know What Inferences Are Needed- Geom, 6th Ed, pg 26

[MichaelM373]

I'm having a very difficult time knowing what I need to infer in order to answer a problem. For example, on page 26 of the Geometry book (6th edition), problem 8

The side of an equilateral triangle has the same length as the diagonal of a square. What is the area of a square?
(1) The height of the equilateral triangle is equal to 6 square root of 3.
(2) The area of the equilateral triangle is equal to 36 square root of 3.

The solution says that you need to know that "the height is always one-half the side times square root of 3". This is not mentioned in the book prior to the problem, so I tried to answer the problem in a different way. This has been a common theme throughout my studies. I am having a hard time recognizing the unstated known of the problems. How do I get better at knowing what I need to infer from the data in a problem in order to answer the question properly? Is there some sort of framework I can follow to make sure I stay on track with an answer?

Thanks for your time.
-Mike

[RonPurewal]

i'm sorry, i'm not really following this.

• what was the information that was not mentioned?

• what was the "other way" in which you tried to solve the problem?

without these specifics, it's impossible to tell what you are saying or what you are asking about.

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• also, please double-check your transcription of the problem—right now it says "What is the area of a square?", which doesn't really make sense. is it supposed to say "the"?

[MichaelM373]

i'm sorry, i'm not really following this.

• what was the information that was not mentioned? "the height is always one-half the side times square root of 3". This is not mentioned in the book prior to the problem

• what was the "other way" in which you tried to solve the problem? [i]Area of the equilateral triangle is given in statement 2. So I tried to work backwards to solve for side of triangle since it was the same as the square. After solving for the side I plugged that into the formula for the area of a square. I didn't actually work the problem out since it was a DS problem. I figured the needed variables could be calculated using the area and deemed this sufficient.[/i]

without these specifics, it's impossible to tell what you are saying or what you are asking about.

__

• also, please double-check your transcription of the problem—right now it says "What is the area of a square?", which doesn't really make sense. is it supposed to say "the"?

Yes, it should be what is the area of "the" square. Everything else is correct.

[Sage Pearce-Higgins]

To solve a problem like this, you just need to apply the basic rules of Geometry. Sure, Geometry is one of the most "knowledge heavy" topics in the quant section, but the cheat sheet at the back of your Geometry Strategy Guide provides all the rules that you need to know.

Of course, applying the rules in the right way is essential, so that when you quote "the height is always one-half the side times square root of 3", it's important to note that this applies only to equilateral triangles (this is covered on p65).

As for your other way of solving the problem, that's totally fine: it's basically the same way as suggested by the explanation on p34. I think that there are two takeaways for you here:
-To know about 30-60-90 triangles (this is the same as an equilateral triangle cut in half).
-To understand what a regular shape is, and to understand that if we know one side of a regular shape, we can find the other sides and the area.

[MichaelM373]

I didn't even notice the cheat sheet. Thanks for the help Sage!

[RonPurewal]

glad we could help you.