Question

Erik draws quadrilateral ABCD. Given it is a parallelogram, then the opposite
sides are congruent. AB = 40x, side BC
= 4 + 3y, side CD = 8x + 32, and side AD
= 9y - 20
What is the value of x?
(1 point)
01
04
• 20
• 40.Given Erik's quadrilateral ABCD and the same measurements as listed
previously. What would the value of y be calculated as? (1 point)
04
08
01
O 16

Answer 1

In a parallelogram, opposite sides are congruent. Therefore, we can set up equations based on the given side lengths.

1. **Set up equations for the sides:**

\[
AB = CD \quad \text{and} \quad BC = AD
\]

From the problem, we have:
- \( AB = 40x \)
- \( CD = 8x + 32 \)
- \( BC = 4 + 3y \)
- \( AD = 9y - 20 \)

2. **First equation (AB = CD):**

\[
40x = 8x + 32
\]

Rearranging gives:

\[
40x - 8x = 32
\]

\[
32x = 32
\]

\[
x = 1
\]

3. **Second equation (BC = AD):**

Now, substitute \( x = 1 \) into the second equation:

\[
4 + 3y = 9y - 20
\]

Rearranging this gives:

\[
4 + 20 = 9y - 3y
\]

\[
24 = 6y
\]

\[
y = 4
\]

4. **Final Answer:**
- The value of \( x \) is \( 1 \).
- The value of \( y \) is \( 4 \).

**To recap:**
- The value of \( x \) is \( 1 \).
- The value of \( y \) is \( 4 \).