Question

The pentagons ABCDE and JKLMN are similarFind the length x of MN.MADM27183827K

Answer 1

Similar Polygons

In similar polygons, the ratio between every pair of corresponding side lengths is equal.

We can see the pentagons ABCDE and JKLMN are similar. Let's find the ratios between their corresponding side lengths:

$\begin{gathered} \frac{AE}{JN}=\frac{2}{1.8} \\ \text{Multiplying by 5:} \\ \frac{AE}{JN}=\frac{10}{9} \end{gathered}$

Also:

$\begin{gathered} \frac{AB}{JK}=\frac{3}{2.7} \\ \text{Dividing by 3 and multiplying by 10:} \\ \frac{AB}{JK}=\frac{10}{9} \end{gathered}$

The ratios of the other side lengths BC/KL and CD/LM are also equal to 10/9.

This helps us to find the value of x because we form an equation with the known proportion as follows:

$\frac{6}{x}=\frac{10}{9}$

Solving for x:

$\begin{gathered} x=\frac{6\cdot9}{10} \\ \boxed{x=5.4^{}} \end{gathered}$