Erik draws quadrilateral ABCD. Given it is a parallelogram, then the opposite

Question

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 \( 4 \).