SSAT Math Question 314: Answer and Explanation
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Question: 314
3. An equilateral triangle has the same perimeter as a circle that has the same perimeter as a square. Which of the following lists the shapes in decreasing order of area?
- A. triangle, square, circle
- B. square, triangle, circle
- C. circle, triangle, square
- D. triangle, circle, square
Correct Answer: E
Explanation:
The answer is E
Write out the formulas for perimeter for each shape: 2πr, 4s, and 3s. Pick a variable, such as r, and manipulate the formulas to put them all in terms of r. For the square, as 2πr = 4s, divide both sides by 4 to find the side length: Ssquare = 
. For the triangle, as 2πr = 3s, divide both sides by 3 to find the side length: Striangle = 
. Now find the area of each shape. The circle is πr2. The square is 
. Multiplying π by itself and dividing by 4 will yield a number less than π because π < 4. Thus, the circle has a gr