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 context of similar triangles, we can set up a proportion based on the corresponding sides of the two triangles.

Let:
- \( a = 11.4 \) inches (side of small triangle)
- \( b = 18 \) inches (side of small triangle)
- \( c = x \) (side of big triangle corresponding to 11.4 inches)
- \( d = 23.4 \) inches (side of big triangle corresponding to 18 inches)

Since the triangles are similar, the ratios of the corresponding sides are equal:

\[
\frac{c}{a} = \frac{d}{b}
\]

Substituting the known values into the equation gives:

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

Now we can solve for \( x \):

1. Cross-multiply to eliminate the fractions:

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

2. Calculate \( 11.4 \cdot 23.4 \):

\[
11.4 \cdot 23.4 = 267.96
\]

3. Now the equation is:

\[
18x = 267.96
\]

4. Divide both sides by 18 to isolate \( x \):

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

5. Carry out the division:

\[
x \approx 14.88
\]

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

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