Question

What is the length of cd

Answer 1

The answer is B.3
This can be done by proportion since the two triangles have same shape but different size.

Answer 2

Answer:

3

Step-by-step explanation:

We can see that both triangles are similar, because they have the same angle of 90º and the angle DCE is equal to the angle BCA then the remain angle it have to be equal. Also we can see that side AC and EC have some proportion. Then we can conclude that the triangles are similar, this means that they have the same shape but different sizes.

To find the side CD we can use a proportion ratio, then the proportion between CA an CE have to the same as the proportion between CB and CD then:

$\dfrac{18}{6}=\dfrac{12-x}{x}$

Now finding x we have:

$\dfrac{18}{6}=\dfrac{12-x}{x}$

$3=\dfrac{12-x}{x}$

$3x=12-x$

$3x+x=12$

$4x=12$

$x=\dfrac{12}{4}=3$