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

Feb 13, 2018

$D E = \frac{5}{2} B C$

#### Explanation:

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:

$\frac{2}{2 + 3} = \frac{2}{5}$

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

$\frac{B C}{D E} = \frac{2}{5}$

...you can cross multiply:

$5 B C = 2 D E$

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

$D E = \frac{5}{2} B C$

GOOD LUCK