Question

What is the length of cd in this diagram ABC ~ EDC.

Answer 1

B) 3

Explanation:

Using the similarity statement, we know that the corresponding sides are AB and ED; AC and EC; BC and DC.

The ratio of sides AB and ED is unknown, since we do not know either side.

The ratio of sides AC and EC is 18/6.

The ratio of sides BC and CD is (12-x)/x.

Since the triangles are similar, the ratio of corresponding sides is equal; this means we can set up a proportion:

`(18)/(6)=(12-x)/(x)`

Cross-multiplying, we have

18(x) = 6(12-x)

Using the dsitributive property, we have

18x = 6(12)-6(x)

18x = 72 - 6x

Adding 6x to each side,

18x+6x = 72-6x+6x

24x = 72

Divide both sides by 24:

24x/24 = 72/24

x = 3

Since the length of CD is x, this means the length of CD is 3.

Answer 2

notice the angles at vertex C, are congruent, and therefore, both triangles are similar by AA, thus


`\bf \cfrac{large}{small}\qquad \cfrac{12-x}{x}=\cfrac{18}{6}\implies 72-6x=18x \\\\\\ 72=24x\implies \cfrac{72}{24}=x\implies 3=x`