Question

solving for unknown values
use parallelogram abcd. what are the values of x and y?
x =
y =
(the parallelogram abcd has side ad labeled 3x - 9, side ab labeled 4y - 3, side bc labeled 42, and side dc labeled 37)

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram, opposite sides are equal in length. So, \( AB = CD \) and \( AD = BC \).

Step2: Solve for \( y \) using \( AB = CD \)

Given \( AB = 4y - 3 \) and \( CD = 37 \). So, we set up the equation:
\( 4y - 3 = 37 \)
Add 3 to both sides: \( 4y = 37 + 3 = 40 \)
Divide both sides by 4: \( y = \frac{40}{4} = 10 \)

Step3: Solve for \( x \) using \( AD = BC \)

Given \( AD = 3x - 9 \) and \( BC = 42 \). So, we set up the equation:
\( 3x - 9 = 42 \)
Add 9 to both sides: \( 3x = 42 + 9 = 51 \)
Divide both sides by 3: \( x = \frac{51}{3} = 17 \)

Answer:

\( x = 17 \)
\( y = 10 \)