https://file.aiquickdraw.com/mathbot/file/1725286134478zled4ret.jpg

To find the values of \( x \) and \( y \) in the parallelogram ABCD, let's analyze the given information and use the properties of parallelograms:

### Given:
- \( AB = 26 \, \text{cm} \)
- \( BC = 18 \, \text{cm} \)
- \( AD = 3x \)
- \( CD = 3y - 1 \)

### Properties of a Parallelogram:
1. Opposite sides of a parallelogram are equal.
2. Therefore, \( AB = CD \) and \( AD = BC \).

### Setting up the equations:
Using the properties of the parallelogram, we can write the following equations:

1. \( AB = CD \)  
   \[
   26 = 3y - 1
   \]

2. \( AD = BC \)  
   \[
   3x = 18
   \]

### Solving the equations:

**1. Solving for \( x \):**

\[
3x = 18
\]

\[
x = \frac{18}{3} = 6
\]

**2. Solving for \( y \):**

\[
26 = 3y - 1
\]

\[
26 + 1 = 3y
\]

\[
3y = 27
\]

\[
y = \frac{27}{3} = 9
\]

### Solution:
- \( x = 6 \)
- \( y = 9 \)

Would you like further details or have any questions?

### Related Questions:
1. What is the perimeter of the parallelogram ABCD?
2. How do you find the area of a parallelogram?
3. What are the different properties of parallelograms?
4. How can you verify if a quadrilateral is a parallelogram?
5. What are the formulas for the diagonals of a parallelogram?

**Tip:** Always use the properties of parallelograms to set up equations when dealing with unknown side lengths.

Learn how to find the values of x and y in parallelogram ABCD using properties and equations. This geometry problem covers key concepts including the properties of parallelograms. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation