Verified Answer :

Nirina7

since BC ∥ DE, we only apply thales theorem, it is

AB / AD =  AC / AE, so we can find directly AE , AB / AD =  AC / AE implies AB x AE  =  AC x AD and  AC= AB x AE  / AD= 12 x 3 /2=18
since AC= 18, and AC=AE+CE, so we can get CE= AC - AE=18-3=15
CE=15cm

The length of CE is 15 m

From the question,

We are to determine the length of CE

In the diagram, ΔADE and ΔABC are similar triangles

By similar triangle theorem, we have that

\(\frac{AD}{BD}=\frac{AE}{CE}\)

From the diagram,

AD = 2 m

BD = 10 m

AE = 3 m

Putting the values into the equation

\(\frac{AD}{BD}=\frac{AE}{CE}\)

We get

\(\frac{2}{10}=\frac{3}{CE}\)

Then, we can write that

\(2 \times CE = 3 \times 10\)

∴ \(CE = \frac{3 \times 10}{2}\)

\(CE =\frac{30}{2}\)

∴ CE = 15 m

Hence, the length of CE is 15 m

Learn more here: https://brainly.com/question/16990281

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