Question

If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale.

Answer 1

Answer:

$x=12\\y=\frac{13}{3}$

Step-by-step explanation:

For it to be a parallelogram, opposite sides have to be of same length.

• OL = NM, and
• ON = LM

Using the expressions given, we can make 2 equations:

Equation 1:

$OL=NM\\3y-6=x-5\\-x+3y=1$

Equation 2:

$ON=LM\\8x-8=7x+4$

Solving equation 2, we have x:

$8x-8=7x+4\\8x-7x=4+8\\x=12$

Plugging this value of x into equation 1, we can solve for y:

$-x+3y=1\\-(12)+3y=1\\-12+3y=1\\3y=13\\y=\frac{13}{3}$

So,

$x=12\\y=\frac{13}{3}$