https://file.aiquickdraw.com/mathbot/file/1726592577509mqtuzb25.jpg

The problem in the image shows a triangle with a perimeter of 17x units. The triangle's sides are labeled as 15 units, 15 units, and 7x units. We are asked to determine which equation can be used to find the value of \( x \).

### Explanation:

The perimeter of a triangle is the sum of the lengths of its three sides. For this triangle, the sides are given as:

- Two sides of 15 units each
- One side of \( 7x \) units

The perimeter is also given as \( 17x \) units.

To find the equation for \( x \), we can set up the perimeter equation as follows:

\[
15 + 15 + 7x = 17x
\]

Simplify the left-hand side:

\[
30 + 7x = 17x
\]

Now, subtract \( 7x \) from both sides:

\[
30 = 17x - 7x
\]

\[
30 = 10x
\]

Finally, solve for \( x \):

\[
x = \frac{30}{10} = 3
\]

### The equation that can be used to find \( x \) is:

\[
30 + 7x = 17x
\]

Would you like more details on the steps or any additional explanation?

Here are 5 related questions to deepen your understanding:
1. What would the perimeter be if \( x = 3 \)?
2. How can you calculate the area of the triangle with the given dimensions?
3. If one of the 15-unit sides is changed to another value, how would that affect the perimeter equation?
4. Can this triangle be classified as an isosceles triangle? Why or why not?
5. How would the equation change if the perimeter was instead \( 20x \) units?

**Tip**: Always check your equations by substituting back the value of \( x \) to verify if the solution satisfies the original conditions.

The perimeter of the triangle shown is 17x units. The dimensions of the triangle are 15 units, 15 units, and 7x units. Which equation can be used to find the value of x?

Learn how to solve for x in a triangle with a perimeter of 17x units and sides measuring 15, 15, and 7x units. This problem involves algebraic concepts, including solving linear equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation