Question

Triangle 1 is a scale drawing of Triangle 2, as shown below.

Triangle 1 has sides 4, x and 6, and triangle 2 has sides 6, 10.5, and 9.

Based on the information shown in these triangles, what is the length of the side x?

Answer 1

To find the length of the side \( x \) in Triangle 1, we start by using the fact that Triangle 1 is a scale drawing of Triangle 2. This means that the sides of Triangle 1 are proportional to the sides of Triangle 2.

Given:
- Triangle 1 sides: \( 4 \), \( x \), \( 6 \)
- Triangle 2 sides: \( 6 \), \( 10.5 \), \( 9 \)

We can set up ratios based on the corresponding sides. Let's take the ratio of the smallest side from Triangle 1 (4) to the smallest side from Triangle 2 (6):

\[
\frac{4}{6} = \frac{2}{3}
\]

Now, we can use this ratio to express side \( x \) in terms of the corresponding side from Triangle 2, which is the second smallest side \( 10.5 \).

Setting up the proportion:

\[
\frac{x}{10.5} = \frac{2}{3}
\]

To find \( x \), we'll cross multiply:

\[
3x = 2 \times 10.5
\]
\[
3x = 21
\]

Now, divide both sides by 3:

\[
x = \frac{21}{3} = 7
\]

Thus, the length of side \( x \) is

\[
\boxed{7}
\]