2020 AMC 8 Problems/Problem 24
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A large square region is paved with gray square tiles, each measuring inches on a side. A border inches wide surrounds each tile. The figure below shows the case for . When , the gray tiles cover of the area of the large square region. What is the ratio for this larger value of
Solution
Let . Then, the total area of the squares of side is , of the area of the large square, which would be , making the side of the large square . Then, borders have a total length of . Since if is the value we're asked to find, the answer is .
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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