The answer for B and explanation? would be nice and Thank you.

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1 Answer
Feb 27, 2018

(a) Yes; and (b) the prism whose base is #DeltaABC# will have greater volume - #6 1/4# times that of #DeltaDEF#.

Explanation:

As #40/16=30/12=5/2#, two adjacent sides are proportional and included angles being right angle are also equal, the two triangles are similar.

As correspoding sides are proportional, areas of similar triangles are in the ratio which is square of the ratio of sides.Hence

#(DeltaABC)/(DeltaDEF)=(5/2)^2=25/4#

As prisms have same height, their volumes are in te proportion of area of their bases.

But bases are #DeltaABC# and #DeltaDEF# are in the ratio #25/4#.

Hence, their volumes will also be in the ratio of #25/4# and the prism whose base is #DeltaABC# will have greater volume and will be #25/4=6 1/4# times volume of prism with base as #DeltaDEF#.