Math
The area of a trapezoid is 66 sq units. The length of its longer base is 4 units longer than the length of its shorter base, and its height is 7 units longer than the length of its shorter base. Find the length of each base and the height of the trapezoid.
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Let x be the length of the shorter base. Then, the length of the longer base = x + 4 The height of the trapezoid = x + 7 Using the formula for finding the area of a trapezoid, Area = x(x + 4) + (x + 7) 66 = x(x + 4) + (x + 7) 66 = x2 + 5x + 7 x2 + 5x - 59 = 0 (x + 17)(x - 3) = 0 x = -17 or x = 3 Since we know that the length of the bases must be positive numbers, x = 3 Length of the shorter base = 3 Length of the longer base = 3 + 4 = 7 Height = 3 + 7 = 10
