https://file.aiquickdraw.com/mathbot/file/1725583956292g5aaymjj.jpg

To solve for \( x \) based on the given diagram of a triangle, I will first analyze the image:

### What we know:
- The triangle has two heights provided: one measuring 6 units and the other 2 units.
- The base length is labeled as \( 12 \) units.
- One of the side lengths is labeled as \( 2x - 2 \).

### Step-by-Step Solution:

This is a right triangle, and we can apply the properties of similar triangles because of the two smaller triangles formed within it (due to the height segments).

#### Step 1: Apply similarity
Since the two triangles formed are similar, the corresponding sides should be proportional.

Let's label the triangles:
- The smaller triangle has a height of 2 and a base of \( 2x - 2 \).
- The larger triangle has a height of 6 and a base of \( 12 \).

We can set up a proportion based on these corresponding sides.

\[
\frac{2}{6} = \frac{2x - 2}{12}
\]

#### Step 2: Solve the proportion

Simplifying the fraction on the left side:

\[
\frac{1}{3} = \frac{2x - 2}{12}
\]

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

\[
1 \cdot 12 = 3 \cdot (2x - 2)
\]

\[
12 = 6x - 6
\]

#### Step 3: Isolate \( x \)

Add 6 to both sides:

\[
18 = 6x
\]

Now, divide by 6:

\[
x = 3
\]

### Conclusion:
The value of \( x \) is \( \boxed{3} \).

Let me know if you'd like more details or have any questions!

Here are 5 related questions:
1. What are the properties of similar triangles?
2. How do you determine corresponding sides in a proportion?
3. Why is cross-multiplication valid in solving proportions?
4. Can this problem be solved using the Pythagorean theorem?
5. How do we verify that the triangles are similar in this problem?

**Tip:** Whenever you encounter a geometric problem, look for similarity or congruence between triangles. These concepts often help simplify complex problems!

Solve for x based on the given triangle, where one part of the height is 6 units, another part is 2 units, the base is 12 units, and one side is labeled as 2x - 2.

Learn how to solve for x in a triangle using the properties of similar triangles. The problem involves proportions, algebra, and geometry. The diagram includes measurements such as a height of 6 units, another height of 2 units, a base of 12 units, and a side labeled as 2x - 2. Suitable for students in 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