Answered

If the sides of one triangle are lengths 2, 4 and 6 and another triangle has sides of lengths 3, 6 and_______, then the triangles are similar.

8

12

9

18

Verified Answer :

avafrankk

the answer is 9 because 2 divided by 3 equals 2/3, 4 divided by 6 equals 2/3, and finally, 6 divided by 9 equals 2/3

Answer:

The correct option is 3.

Step-by-step explanation:

The corresponding sides of similar triangles are similar.

It is given that two triangles are similar. One triangle are lengths 2, 4 and 6 and another triangle has sides of lengths 3, 6 and x.

Since the corresponding sides of similar triangles are proportional, therefore

\(\frac{2}{3}=\frac{4}{6}=\frac{6}{x}\)

\(\frac{2}{3}=\frac{2}{3}=\frac{6}{x}\)

\(\frac{2}{3}=\frac{6}{x}\)

Use cross multiplication.

\(2\times x=6\times 3\)

\(2x=18\)

Divide both sides by 2.

\(x=\frac{18}{2}\)

\(x=9\)

Therefore the correct option is 3.

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