Question 1068988: The area of a triangle can be found by using the formula 𝐴 = 1/2 𝑏ℎ. The area of the triangle can be represented by the expression −17.5𝑥2 − 138.5𝑥 − 27. The triangle’s base length is greater than its height. If the area of the triangle is 231 square inches, find the value of x as it relates to this rectangle, the numerical length of the base, and the numerical length of the height.
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! −17.5𝑥^2 − 138.5𝑥 − 27 = 231
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multiply both sides of = by "-"
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17.5x^2 + 138.5x +27 = -231
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add 231 to both sides of =
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17.5x^2 + 138.5x +258 = 0
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divide both sides of = by 5
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3.5x^2 + 27.7x + 51.6 = 0
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use quadratic formula to solve for x
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x = -3 and x = approximately -4.9
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we accept x = -3 since -4.9 is an approximation
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factors of 231 are 1,3,7,11,21,33,77,231
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base > height which eliminates 1, 3, 7, 11 as base, therefore we have
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the following pairs of base, height are valid for the triangle (42,11), (66, 7), (154, 3), (462, 1)
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Answer by ikleyn(52793)  (Show Source):
You can put this solution on YOUR website! .
1. In the condition, the notions "triangle" and "rectangle" are missed.
2. Finding "x" is not related (and is not relevant) to finding the base length and the height length.
3. There are INFINITELY MANY other solutions, different from integers.
The Diagnosis. This problem is NONSENSE in degree 3.
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