https://file.aiquickdraw.com/mathbot/file/17266247466644thlfosb.jpg

These two triangles are similar with a scale factor of three. Solve for the side x.

The diagram shows two similar triangles, with the given information indicating that the scale factor between the two triangles is 3. The smaller triangle has sides of 4, 6, and 8 units, while the larger triangle has one unknown side, \( x \).

Given that the triangles are similar, corresponding sides are proportional. This means that the ratio of corresponding sides in the two triangles should be equal to the scale factor.

The side corresponding to \( x \) in the smaller triangle is 6 (as indicated by the base). Therefore, using the scale factor of 3, the relation is:

\[
\frac{x}{6} = 3
\]

Multiplying both sides by 6 to solve for \( x \):

\[
x = 3 \times 6 = 18
\]

Thus, the value of \( x \) is 18 units.

Would you like more details on how similar triangles work or on proportionality? Here are some related questions you can explore:

1. What are the properties of similar triangles?
2. How do you calculate the scale factor between two triangles?
3. How do the angles in similar triangles relate to each other?
4. Can the Pythagorean theorem be applied to triangles that are not right-angled?
5. How do you find missing sides using trigonometric ratios?

**Tip**: Always check the corresponding angles when working with similar triangles to confirm the correct proportional sides.

Solve for the missing side of a triangle using similarity and proportionality. This problem explores the properties of similar triangles and how to apply the scale factor to find unknown sides. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation