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# A sculptor is planning to make two triangular prisms out of steel.

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A sculptor is planning to make two triangular prisms out of steel. The sculptor will use ΔLMN for the bases of one prism and ΔWXY for the bases of the other prism.

1. Is ΔLMN similar to ΔWXY?  Explain.
2. Suppose the sculptor makes both prisms with the same height. Which prism will have a greater volume? How many times greater? Show all your work.
Mar 15, 2021

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1.  Yes, △LMN is similar to △WXY because  21/30  =  7/10  =  28/40  and the included angles are equal because they are both 90°, so by the SAS similarity theorem, the two triangles are similar.

2. The one with the larger base, which is the one with △WXY as the base, will have the greater volume.

volume of smaller prism  =   (area of base) * (height)

volume of smaller prism   =   (1/2 * 30 * 21) * (height)

volume of smaller prism   =   (315) * (height)

volume of smaller prism   =   315h        ,  where  h  is the height of the prism

volume of larger prism   =   (area of base) * (height)

volume of larger prism   =   (1/2 * 40 * 28) * (height)

volume of larger prism   =   (560) * (height)

volume of larger prism   =   560h

The larger prism is how many times greater than the smaller prism? That is,  560h  is how many times greater than  315h  ?

560h/315h   =   16/9         so...         560h  =  (16/9) * 315h

In other words,  560h  is  16/9  times  315h ,  which means the volume of the larger larger prism is  16/9  times the volume of the smaller prism.

Mar 15, 2021