2011 AMC 10B Problems/Problem 14
Problem
A rectangular parking lot has a diagonal of meters and an area of square meters. In meters, what is the perimeter of the parking lot?
Solution
Let the sides of the rectangular parking lot be and . Then and . Add the two equations together, then factor. The perimeter of a rectangle is
Solution 2 (Quick)
We see the answer choices or the perimeter are integers. Therefore, the sides of the rectangle are most likely integers that satisfy . In other words, is a set of Pythagorean triples. Guessing and checking, we have as the triplet, as the area is as requested. Therefore, the perimeter is .
See Also
2011 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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