Question

triangle 1: side length of 11.4 in. and 18 in.
tringle 2: side length of 23.4 in. and x
What is the length of x in decimal form to the nearest hundredth?
(1 point)
inches

Answer 1

To determine the length of side \( x \) in triangle 2, we can use the concept of similar triangles or the triangle inequality theorem. However, we need more information to make an accurate conclusion; typically, we would have a relation such as whether the triangles are similar or if there is an additional side length or angle given.

Assuming that triangle 1 and triangle 2 are similar triangles based on the given side lengths, we can find the corresponding sides and set up a proportion:

Given:
- Triangle 1 has sides of lengths 11.4 in and 18 in.
- Triangle 2 has one side of 23.4 in and side \( x \).

We can set up the proportion based on corresponding sides:
\[
\frac{11.4}{23.4} = \frac{18}{x}
\]

Now, cross-multiply:
\[
11.4 \cdot x = 18 \cdot 23.4
\]

Calculating the right side:
\[
18 \cdot 23.4 = 421.2
\]

So we have:
\[
11.4x = 421.2
\]

Now, divide both sides by 11.4 to solve for \( x \):
\[
x = \frac{421.2}{11.4}
\]

Calculating this gives:
\[
x \approx 36.92
\]

Thus, the length of \( x \) in decimal form to the nearest hundredth is **36.92 inches**.