Question

a triangle shows 11.4 inch on one side and 18 inch on the other. another triangle shows x on one side and 23.4 inch on the other.

what is the length of x in decimal form to the nearest hundredth?

Answer 1

To find the length of \(x\) in the second triangle, we need to establish a relationship between the two triangles based on their corresponding sides.

We are given:
- One triangle has sides 11.4 inches and 18 inches.
- The other triangle has sides \(x\) and 23.4 inches.

If we assume that the triangles are similar, we can set up a proportion based on the lengths of the sides:

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

Now, we can solve for \(x\). First, we calculate the ratio on the right:

\[
\frac{11.4}{18} = 0.6333... \quad (\text{approximately } 0.6333)
\]

Now we rewrite the proportion:

\[
\frac{x}{23.4} = 0.6333
\]

To solve for \(x\), we cross-multiply:

\[
x = 23.4 \times 0.6333
\]

Calculating that gives:

\[
x \approx 14.85382
\]

Now, rounding this to the nearest hundredth:

\[
x \approx 14.85
\]

Therefore, the length of \(x\) is approximately **14.85 inches**.