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Applications of Quadratic Equations - Problem 5

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Areas of shapes in geometry often involve quadratic relationships because areas are found by multiplying relationships between the sides of shapes. Here we look at how quadratics show up in problems related to the areas of triangles and rectangles. Start by setting up an equation for the area, then set it equal to zero in order to solve by factoring or the quadratic formula. Make sure your answer makes sense- often we get two solutions, but only one of them will make sense as a side length. (That is, a side length could never be negative, so check your final solutions!)

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