## Example Questions

### Example Question #21 : Geometry

The formula to find the radius of the largest circle that can fit in an equilateral triangle is , where is the length of any one side of the triange.

What is the largest diameter of a circle that can fit inside an equilateral triangle with a perimeter of cm? cm cm cm cm cm

Explanation:

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 = = 2.89 cm

### Example Question #21 : Plane 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?

The relationship of the quantities cannot be determined.

Quantity B is larger.

Quantity A is larger.

Both quantities are equal.

Quantity B is larger.

Explanation:

Consider each quantity separately.

Quantity A

Recall that the area of a circle is defined as: We know that the area is . Therefore, Divide both sides by : Therefore, . Since , we know: Quantity B

This is very easy. Recall that: Therefore, if  . Therefore, Quantity B is larger.

### Example Question #22 : Plane 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.

The relationship between the quantities cannot be determined.

The two quantities are equal.

Quantity A is larger.

Quantity B is larger.

Explanation:

Consider each quantity separately.

Quantity A

Recall that the area of a circle is defined as: We know that the area is . Therefore, Divide both sides by : Therefore, .  Since , we know: 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 is . Therefore, .  This means that . Therefore, Quantity B is larger.

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