Question

What's the length of CD?

Image attached below.

Answer 1

Notice that two angles of the large triangle are congruent to two angles of the small triangle.
What does that mean about the triangles?

Answer 2

They are congruent, right?

Answer 3

Not, congruent, but similar.
Congruent means same size and shape.
Similar means same shape without having to be the same size.

Answer 4

When two triangles are similar, the lengths of corresponding sides are in the same ratio.

Answer 5

That means the ratio of BC to CD is equal to the ratio of AC to CE.

Answer 6

\(\dfrac{BC}{CD} = \dfrac{AC}{CE} \)

Now replace each of those segment lengths with the length shown in the figure.

Answer 7

Then solve for x.

Answer 8

Is the answer 1.5?

Answer 9

I don't know until I solve it.

Answer 10

\(\dfrac{BC}{CD} = \dfrac{AC}{CE}\)

\(\dfrac{16-x}{x} = \dfrac{18}{6}\)

You need to solve the proportion above.
Cross multiply and solve for x.

Answer 11

so it's 4.

Answer 12

\(\dfrac{16-x}{x} = \dfrac{3}{1}\)

\(3x =16 - x\)

\(4x = 16\)

\(x = 4\)

Correct!

Answer 13

Thanks a bunch.

Answer 14

You're welcome.