2018 UNCO Math Contest II Problems/Problem 2
Segment AB is perpendicular to segment BC and segment AC is perpendicular to segment BD. If segment AB has length 15 and segment DC has length 16, then what is the area of triangle ABC?
Let the altitude be called , be called , and called . Since is a right triangle, we can write a system of equations.
Solving the second equation, we get or . Since has to be positive, . Plugging into the first equation, we get that or . Once again, side lengths must be positive, so . Now we have an altitude and a base, so the area of is
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