GRE Math : How to find the length of the diameter
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Example Questions
Example Question #1 : Diameter
The formula to find the radius of the largest circle that can fit in an equilateral triangle is 
What is the largest diameter of a circle that can fit inside an equilateral triangle with a perimeter of 
The diameter is
To solve for the largest diameter multiply each side by 2.
The resulting formula for diamenter is
Substitute in 5 for S and solve. Diameter = 
Example Question #2 : Diameter
Quantity A: The diameter of a circle with area of
Quantity B: The diameter of a circle with circumference of
Which of the following is true?
Quantity B is larger.
The relationship of the quantities cannot be determined.
Quantity A is larger.
Both quantities are equal.
Quantity B is larger.
Consider each quantity separately.
Quantity A
Recall that the area of a circle is defined as:
We know that the area is 
Divide both sides by 
Therefore, 
Quantity B
This is very easy. Recall that:
Therefore, if 
Example Question #1 : How To Find The Length Of The Diameter
Quantity A: The diameter of a circle with area of
Quantity B: The diameter of a circle with circumference of
Which of the following is true?
The relationship between the quantities cannot be determined.
The two quantities are equal.
Quantity B is larger.
Quantity A is larger.
Quantity B is larger.
Consider each quantity separately.
Quantity A
Recall that the area of a circle is defined as:
We know that the area is 
Divide both sides by 
Therefore, 
Quantity B
This is very easy. Recall that:
Therefore, if 
Now, since your calculator will not have a square root button on it, we need to estimate for Quantity A. We know that 
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