Skip to main content

2017 AMC 10A Problem 3

Problem 3 of 25EasierGeometry

Tamara has three rows of two 66-feet by 22-feet flower beds in her garden. The beds are separated and also surrounded by 11-foot-wide walkways, as shown on the diagram. What is the total area of the walkways, in square feet?

Answer choices

Show solution

Solution

We can see that the width of the garden is 2⋅6+3⋅1=15.2 \cdot 6 + 3 \cdot 1 = 15. We can also see that the height is 3⋅2+4⋅1=10. 3 \cdot 2 + 4 \cdot 1 = 10. The total area of the garden is therefore 15⋅10=150.15 \cdot 10 = 150. The area of all the flower beds is 6⋅2⋅6=72. 6 \cdot 2 \cdot 6 = 72. Subtracting this from the area of the garden yields 150−72=78,150 - 72 = 78, which is the area of the walkways. Thus, B is the correct answer.
AoPS wiki

Tagged: area decomposition · rectangle

More practice