Question

Question

Use the image to answer the 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
?

Answer 1

Since the two quadrilaterals are similar, their corresponding sides are proportional.

We know the following measurements:

• In the small quadrilateral, one side measures 2, and the opposite side measures 5.
• In the big quadrilateral, the corresponding side to 2 measures 3.6, and the corresponding side to 5 measures $x$.

We can set up the proportion based on the corresponding sides:

$$\frac{2}{5}=\frac{3.6}{x}$$

To solve for $x$, we cross-multiply:

$$2x=5\times 3.6$$

Calculating the right side:

$$5\times 3.6=18$$

Now we have:

$$2x=18$$

Next, we solve for $x$ by dividing both sides by 2:

$$x=\frac{18}{2}=9$$

Thus, the value of $x$ is $\boxed{{\displaystyle 9}}$.