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For the pair of similar triangles, find the value of x

To find the value of \( x \) for the pair of similar triangles, we will use the property that corresponding sides of similar triangles are proportional.

Given triangles are similar, their corresponding side lengths are proportional. For the triangles shown:

- Larger triangle: sides are \( 2x - 4 \), \( 39 \)
- Smaller triangle: sides are \( x + 6 \), \( 24 \)

We can set up the proportion:

\[
\frac{2x - 4}{39} = \frac{x + 6}{24}
\]

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

\[
(2x - 4) \cdot 24 = 39 \cdot (x + 6)
\]

Expanding both sides:

\[
48x - 96 = 39x + 234
\]

Next, we solve for \( x \):

\[
48x - 39x = 234 + 96
\]

\[
9x = 330
\]

\[
x = \frac{330}{9}
\]

\[
x = \frac{110}{3}
\]

So, the value of \( x \) is \( \frac{110}{3} \) or approximately 36.67.

Would you like more details or have any other questions?

Here are some more questions you might be interested in:

1. How do you prove two triangles are similar?
2. What is the Pythagorean theorem and how is it used?
3. How do you find the area of a triangle?
4. How can you solve quadratic equations?
5. What are the properties of right triangles?

**Tip:** When working with similar triangles, always ensure you correctly identify and match corresponding sides to set up accurate proportions.

Learn how to find the value of x for a pair of similar triangles using proportions and cross-multiplication. This problem involves identifying corresponding sides of similar triangles and setting up a proportion to solve for x. Suitable for Grades 7-9.

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