In the below diagram, BC is parallel to DE. Given AC:CE=2:3, express $vecDE$ in term of $vecBC$ ?

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Answer 1 · 2018-02-13T12:56:13

$DE = 5/2BC$

If BC is parallel to DE, then the triangles are similar, which means that all sides are proportional.

We are given that AC:CE = 2:3

So, the ratio of AC to the comparable side of the larger triangle, which is AE = AC + CE is:

$2/(2+3) = 2/5$

So, they are similar triangles, so BC/DE is the same ratio:

$(BC)/(DE) = 2/5$

...you can cross multiply:

$5BC = 2DE$

...and then you can write an equation for DE in terms of BC:

$DE = 5/2BC$

GOOD LUCK

In the below diagram, BC is parallel to DE. Given AC:CE=2:3, express vecDEvecDE in term of vecBCvecBC?