GRE Math : How to find the length of the diameter
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Example Questions
Example Question #1 : How To Find The Length Of The 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 #22 : Geometry
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.
Quantity A is larger.
The relationship of the quantities cannot be determined.
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 #2 : 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?
Quantity B is larger.
Quantity A is larger.
The two quantities are equal.
The relationship between the quantities cannot be determined.
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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