https://file.aiquickdraw.com/mathbot/file/1725977764223cocrbw8k.jpg

To solve for the length of \( AB \) in the triangle, we can use the given information about angles and side lengths.

The triangle has:

- \( \angle A = 50^\circ \)
- \( \angle C = 50^\circ \)
- \( AB = 4x \)
- \( BC = 2x + 6 \)

Since the angles at \( A \) and \( C \) are both \( 50^\circ \), the triangle is isosceles. This means that the sides opposite those angles must be equal. Therefore, \( AB = BC \).

### Setting up the equation:

\[
4x = 2x + 6
\]

Now, solve for \( x \):

1. Subtract \( 2x \) from both sides:

\[
4x - 2x = 6
\]
\[
2x = 6
\]

2. Divide both sides by 2:

\[
x = 3
\]

### Finding the length of \( AB \):

Since \( AB = 4x \), substitute \( x = 3 \) into this expression:

\[
AB = 4(3) = 12
\]

Thus, the length of \( AB \) is 12. The correct answer is **C. 12**.

---

Would you like a more detailed explanation of the isosceles triangle property or any other aspect of this problem?

Here are five related questions you might explore:

1. What is the sum of the angles in any triangle, and why?
2. How would you find the perimeter of this triangle?
3. What would happen if \( \angle A \) and \( \angle C \) were not equal?
4. How can you apply the Law of Sines to solve triangles with non-right angles?
5. If you knew the area of the triangle, how would you find the height?

**Tip:** When solving for unknowns in isosceles triangles, always use the property that two sides (opposite equal angles) are congruent—it simplifies the equation.

What is the length of AB in the triangle with angles at A and C both equal to 50 degrees, and side lengths AB = 4x and BC = 2x + 6?

Solve this isosceles triangle problem where angles A and C are both 50 degrees, and the sides AB and BC are represented as algebraic expressions. Learn how to set up the equation 4x = 2x + 6 and solve for the length of AB. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation