Mathematics

Mathematics

Problem

In △ABC\triangle ABC, let AB=18 cmAB=18\,\text{cm} and AC=24 cmAC=24\,\text{cm}. A point DD on ABAB is chosen so that AD=8 cmAD=8\,\text{cm}. For DEDE (where EE is on ACAC) to be parallel to BCBC, what is the only correct statement about the length of AEAE? a) AE=10 cmAE=10\,\text{cm} makes DE∥BCDE\parallel BC. b) No integer length of AEAE can make DE∥BCDE \parallel BC. c) AE=11 cmAE=11\,\text{cm} makes DE∥BCDE\parallel BC. d) AE=8 cmAE=8\,\text{cm} makes DE∥BCDE\parallel BC.

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