the height of a rectangular prism is 3ft. the length and width can be expressed as x-1 and x+4. if the volume of the prism is 198ft^3, find the value of x

Respuesta :

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Formula
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Volume = Length x Width x Height

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Apply Formula
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198 = 3(x-1)(x+4)

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Divide by 3 through
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66 = (x-1)(x+4)

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Remove brackets
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66 = x² + 4x - x - 4
66 = x² + 3x - 4

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Take away 66 from both sides
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0 = x² + 3x - 4 - 66
x² + 3x - 70 = 0

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Factorise the quadratic
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(x - 7)(x + 10) = 0
x = 7 or x = -10 (rejected, length cannot be negative)

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Answer : x = 7
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