Question

The two quadrilaterals are similar. What is the value of x?

1. Quadrilateral 2 and 5
2. Quadrilateral 3.6 and x

Answer 1

To determine the value of \( x \) in the context of similar quadrilaterals, we can use the property that corresponding sides of similar figures are proportional.

Let's say we have:

1. Quadrilateral 2 has a side length of \( 2 \) (this is assumed).
2. Quadrilateral 5 has a corresponding side length of \( 5 \).

From the similarity of quadrilaterals, the ratio of their corresponding sides can be set up as follows:

\[
\frac{\text{Side length of Quadrilateral 2}}{\text{Side length of Quadrilateral 5}} = \frac{2}{5}
\]

Next, if we consider another pair:

1. Quadrilateral 3.6 has a side length of \( 3.6 \) (this is also assumed).
2. Quadrilateral \( x \) has a corresponding side length of \( x \).

Using the same principle, we would express this proportion as:

\[
\frac{3.6}{x} = \frac{2}{5}
\]

Now, we can cross-multiply to solve for \( x \):

\[
2x = 5 \times 3.6
\]

Calculating \( 5 \times 3.6 \):

\[
5 \times 3.6 = 18
\]

Thus, the equation simplifies to:

\[
2x = 18
\]

Dividing both sides by \( 2 \):

\[
x = \frac{18}{2} = 9
\]

Therefore, the value of \( x \) is \( \boxed{9} \).