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12 March, 02:43

Select the correct answer. The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, which equation models this situation? A. 6x2 + x - 12 = 0 B. 6x2 + x - 13 = 0 C. 6x2 + x - 26 = 0 D. 36x2 + 6x - 26 = 0

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  1. 12 March, 03:09
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    Answer: The correct answer is C: 6x² + x - 26 = 0

    Step-by-step explanation: All the variables in the question have been identified, that is, the area, the height and the base of the triangle. The area of a triangle is defined as

    Area = ½ x B x H

    Area = 13,

    Base = B and

    Height = 6B + 1

    The question states that the height is 1 more than 6 times it's base. Hence the height would be, Base x 6, plus 1, that is, 6B + 1

    The area can now be expressed properly as follows,

    13 = ½ x B x (6B + 1)

    By cross multiplication we now have

    2 x 13 = B (6B + 1)

    26 = 6B² + B

    Subtract 26 from both sides of the equation

    6B² + B - 26 = 0

    However, the answer uses x as the unknown variable. So if you use x as the base of the triangle instead of B, your answer would result in

    6x² + x - 26 = 0
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