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jmc

prealgebra senior

Problem

A rhombus has a perimeter of units and one of its diagonals is units. What is its area in square units?
Solution
If a rhombus has a perimeter of 68 units, then its side length must be 17. Since diagonals of a rhombus are perpendicular bisectors of each other, the right triangle that is formed has one leg of length 15 and another leg of length 8. Therefore, the area of one of the right triangles is , so since the rhombus is made up of four congruent right triangles, the area of the rhombus is .
Final answer
240