Question

Given quadrilateral ABCD is similar to quadrilateral EFGH, calculate the length of CD.

A. 7
B. 8
C. 9
D. 2

Answer 1

Well if you were to turn these to be in the same direction and everything you would see the side lengths ratios.

\[\large AB = EF \space \space \space BC = GF \space \space \space AD = HE \space \space \space DC = HG\]

So we just need to set up 1 proportion.

Let's compare GF and BC and use that to solve HG = DC.

\[\large \frac{ 7.5 }{ 4 } = \frac{ 15 }{ DC }\]


To solve for DC:

Remember when you cross multiply. You do 7.5 * DC and 15 * 4.

So then we have

\[\large 7.5DC = 60\]

Now divide both sides by 7.5
Answer: 8