Use the image to answer the question.

Question

An illustration shows two quadrilaterals, one big and one small. In the small quadrilateral, one side measures 2 and its opposite side measures 5. In the big quadrilateral, the side corresponding to 2 in the small quadrilateral measures 3.6 and the side corresponding to 5 measures x.

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

(1 point)

Answer 1

In similar figures, the ratios of corresponding sides are equal.

Given the sides of the small quadrilateral:

• One side = 2
• Opposite side = 5

For the big quadrilateral:

• Corresponding side to 2 = 3.6
• Corresponding side to 5 = x (which we want to find)

Using the ratio of the corresponding sides, we have:

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

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

\[ 2x = 3.6 \cdot 5 \]

Calculating the right side:

\[ 3.6 \cdot 5 = 18 \]

So, we have:

\[ 2x = 18 \]

Now, divide both sides by 2:

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

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