If pentagon ABCDE is similar to pentagon FGHIJ, and AB = 10, CD = 5, and FG = 30, what is IH?

Explanation

If both shapes are similar, then the sides are in proportion. Because AB is similar to FG,
and AB = 10 and FG = 30, the second pentagon is three times as large as the first pentagon. Therefore, IH is three times as large as CD, which gives a length of 15.

You could solve it also as two equal ratios

\(\frac{CD}{AB} = \frac{IH}{FG}\)

So

IH = \(\frac{CD}{AB} * FG = \frac{5}{10} * 30 = 15 \)