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: Use property of parallelogram diagonals

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

Step2: Solve for $y$

Set up the equation $y + 3=3y - 1$.
Subtract $y$ from both sides: $3 = 2y-1$.
Add 1 to both sides: $4 = 2y$.
Divide both sides by 2: $y = 2$.

Step3: Solve for $x$

Since $MP = OP$ and $MP = 21$ m, then $2x-1=21$.
Add 1 to both sides: $2x=22$.
Divide both sides by 2: $x = 11$.

Answer:

$x = 11$ m, $y = 2$ m