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| − | ==Problem==
| + | #Redirect [[2012 CEMC_Gauss (Grade 8) Problems/Problem_18]] |
| − | A triangular prism has a volume of <math>120 cm^{3}</math>. Two edges of the triangular prism measure 3 cm and 4 cm, as shown.
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| − | The height of the prism, in cm, is
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| − | <math>\text{(A)}\ 12 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 8 </math>
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| − | ==Solution==
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| − | The volume of the triangular prism will be the area of the base multiplied by its height.
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| − | Let <math>A</math> and <math>h</math> be the area of the base and the height, respectively. We then have:
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| − | <math>A = \frac{3 cm * 4 cm}{2} = 6 cm^2</math>
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| − | <math>A * h = V</math>
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| − | <math>6 cm^2 * h = 120 cm^3</math>
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| − | <math>h = \frac{120 cm^3}{6 cm^2} = 20 cm</math>
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| − | Thus, the answer is <math>\boxed {\textbf {(B) } 20}</math>.
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