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jmc

geometry intermediate

Problem

Each vertex of this parallelogram has integer coordinates. The perimeter of this parallelogram is units, while the area is square units. What is the value of the sum ?

problem
Solution
The length of the bottom side of the parallelogram is 7 units, and the length of the left side of the parallelogram is units, by the Pythagorean theorem. Since the opposite two sides are congruent to these two, the perimeter of the parallelogram is units. The area of the parallelogram is equal to its base times its height, which is square units. Therefore, .
Final answer
52