Question

in parallelogram lmno, mp = 21 m, lp = (y + 3) m, np = (3y − 1) m, and op = (2x − 1) m. what are the values of x and y?
○ x = 10 m, y = 1 m
○ x = 10 m, y = 2 m
○ x = 11 m, y = 1 m
○ x = 11 m, y = 2 m

Explanation:

Step1: Recall parallelogram diagonals property

In a parallelogram, the diagonals bisect each other. So, \( LP = NP \) and \( MP = OP \).

Step2: Solve for \( y \) using \( LP = NP \)

Given \( LP=(y + 3)\) m and \( NP=(3y - 1)\) m. Set them equal:
\( y + 3=3y - 1 \)
Subtract \( y \) from both sides: \( 3 = 2y - 1 \)
Add 1 to both sides: \( 4 = 2y \)
Divide by 2: \( y = 2 \)

Step3: Solve for \( x \) using \( MP = OP \)

Given \( MP = 21 \) m and \( OP=(2x - 1)\) m. Set them equal:
\( 2x - 1 = 21 \)
Add 1 to both sides: \( 2x = 22 \)
Divide by 2: \( x = 11 \)

Answer:

\( x = 11 \) m, \( y = 2 \) m (the option: \( x = 11 \) m, \( y = 2 \) m)