SOLUTION: A triangle has an area of 28 square inches. The base of the triangle is 6 inches less tham twice the hieght. What is the length o the base o the triangle?
I keep getting 7, but
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-> SOLUTION: A triangle has an area of 28 square inches. The base of the triangle is 6 inches less tham twice the hieght. What is the length o the base o the triangle?
I keep getting 7, but
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Question 537495: A triangle has an area of 28 square inches. The base of the triangle is 6 inches less tham twice the hieght. What is the length o the base o the triangle?
I keep getting 7, but the correct answer is 8? I'm not sure if that is correct or if I'm doing something wrong. Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! I suspect that you may have stopped working too soon. The height is 7. But you were asked to find the base. Since the base is twice the height minus 6, you multiply the height by 2 to get 14 and then you subtract 6 to get the base. So the base is 14 minus 6 = 8.
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You get the height by using the equation:
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Area = (1/2)B*H
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You are told that the base (B) equals twice the height minus 6. So you can write:
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B = 2H - 6
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Substitute the right side of this equation for B in the area equation to get:
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Area = (1/2)(2H - 6)H
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Multiply out the right side and you get:
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Area = (2H^2 - 6H)/2 = H^2 - 3H
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Replace Area with its value 28:
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28 = H^2 - 3H
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Subtract 28 from both sides to get the standard quadratic form:
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H^2 - 3H - 28 = 0
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Factor the left side:
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(H - 7)*(H + 3) = 0
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Set the two factors equal to zero and you find that H = 7 and H = -3 are solutions to this quadratic equation. H = -3 makes no sense (a negative height??). So the only valid solution is H = 7, and this leads to the Base being 8 as described up above.
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Hope this helps.
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