# If LMNO is a parallelogram, what are the values of x and y if ON=5x-7, LM = 4x +4, and NM = x-7?

Dec 17, 2017

Considering $O L = y$
$x = 11 \mathmr{and} y = 4$

#### Explanation:

Given that :
$O N = 5 x - 7 , L M = 4 x + 4 , \mathmr{and} N M = x - 7$

In the parallelogram$L M N O$,
Side$L M$ is opposite and parallel to side $O N$ and will have equal lengths according to the properties of a parallelogram.

$\therefore O N = L M$

$\implies 5 x - 7 = 4 x + 4$

$\implies 5 x - 4 x = 4 + 7$

$\implies x = 11$

If side $O L = y$,
then

$N M$ will be parallel to $O L$

And as $N M$ and side $O L$ are opposite sides of a parallelogram , they will have equal lengths.

$\therefore N M = O L$

$\implies x - 7 = y$

$\implies y = 11 - 7 = 4$

Answer : $x = 11 \mathmr{and} y = 4$