Difference between revisions of "2012 CEMC Gauss (Grade 7) Problems/Problem 21"

Latest revision as of 21:02, 18 October 2025

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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}. Two edges of the triangular prism measure 3 cm and 4 cm, as shown.
-{{Template:Image needed}}
-The height of the prism, in cm, is
-</math>\text{(A)}\ 12 \qquad \text{(B)}\ 20 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 16 \qquad \text{(E)}\ 8 <math>
-==Solution==
-The volume of the triangular prism will be the area of the base multiplied by its height.
-Let </math>A<math> and </math>h<math> be the area of the base and the height, respectively. We then have:
-</math>A = \frac{3 cm * 4 cm}{2} = 6 cm^2<math>
-</math>A * h = V<math>
-</math>6 cm^2 * h = 120 cm^3<math>
-</math>h = \frac{120 cm^3}{6 cm^2} = 20 cm<math>
-Thus, the answer is </math>\boxed {\textbf {(B) } 20}$.