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?

__ inches

Answer 1

To find the length \( x \) for the corresponding side in the big triangle, we can use the concept of similarity of triangles. The ratio of the lengths of corresponding sides in similar triangles is constant.

Given:
- Small triangle sides: \( 11.4 \) inches and \( 18 \) inches.
- Big triangle sides: \( x \) (corresponding to \( 11.4 \) inches) and \( 23.4 \) inches (corresponding to \( 18 \) inches).

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

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

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

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

Calculating the product on the right side:

\[
11.4 \cdot 23.4 = 267.96
\]

Now we can substitute this back into the equation:

\[
18x = 267.96
\]

Next, we solve for \( x \) by dividing both sides by \( 18 \):

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

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

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