Question

An illustration shows two triangles, one big and one small. In the small triangle, one side measures 11.4 inches and another side measures 18 inches. In the big triangle, the side corresponding to 11.4 inches in the small triangle measures x and the side corresponding to 18 inches measures 23.4 inches.

What is the length of x in decimal form to the nearest hundredth?
(1 point)
inches

Answer 1

To solve for \( x \) in the big triangle using the sides of the small triangle, we can use the property of similar triangles. The sides of similar triangles are proportional.

Given:
- In the small triangle:
- One side = 11.4 inches
- Another side = 18 inches

- In the big triangle:
- Side corresponding to 11.4 inches = \( x \)
- Side corresponding to 18 inches = 23.4 inches

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

\[
\frac{x}{11.4} = \frac{23.4}{18}
\]

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

\[
x \cdot 18 = 11.4 \cdot 23.4
\]

Calculating \( 11.4 \cdot 23.4 \):

\[
11.4 \times 23.4 = 267.96
\]

So now our equation is:

\[
18x = 267.96
\]

Now divide both sides by 18 to solve for \( x \):

\[
x = \frac{267.96}{18} \approx 14.88
\]

Thus, the length of \( x \) in decimal form to the nearest hundredth is:

\[
\boxed{14.88} \text{ inches}
\]