Question

The triangle share the exact same shape
Triangle one right side 11.4 in bottom 18 in
Triangle 2 right side x bottom 23.4 in

What is the length of x in decimal form to the nearest hundredth

Answer 1

Since the triangles share the same shape, they are similar triangles. We can set up a proportion based on their corresponding sides.

For Triangle 1:
- Right side = 11.4 inches
- Bottom = 18 inches

For Triangle 2:
- Right side = \( x \) inches
- Bottom = 23.4 inches

We can set up the proportion:

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

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

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

Calculating \( 11.4 \cdot 23.4 \):

\[
11.4 \cdot 23.4 = 267.96
\]

So we have:

\[
267.96 = 18x
\]

Now, divide both sides by 18 to isolate \( x \):

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

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

\[
\boxed{14.88}
\]