ISEE Word Problems Question 212: Answer and Explanation
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Question: 212
5. Use the figure below to answer the question.
If arc PQR is a semicircle, what is the perimeter of PQRS?
- A. 17 +
π - B. 17 +
π - C. 30 +
π - D. 30 +
π
Correct Answer: A
Explanation:
The answer is A
To find the perimeter of PQRS, you need the measure of the arc, which is part of the semicircle. The diameter of the semicircle is the hypotenuse of the triangle, so use the Pythagorean theorem (or recognize the Pythagorean triple) to find that the diameter is 13. The measure of the arc is half the circumference, so write an equation with 13 as the diameter: 
πd = 13π = 
π. Add this to the sum of the legs of the triangle to find the perimeter: 17 + π.