Parallelogram LMNO has two diagonal lines, LN and MO, that intersect at P. The length of LP can be expressed by 3x-4, and PN by the expression x + 14 Identify a pattern regarding the diagonals of the parallelogram to find the value of x. (1 point)

Answer 1

In a parallelogram, the diagonals bisect each other. This means that the lengths of the segments formed by the intersection of the diagonals at point P are equal.

In this problem, we have:

• $LP$ is expressed as $3x-4$
• $PN$ is expressed as $x+14$

Since diagonals bisect each other, we can set the lengths of $LP$ and $PN$ equal to each other:

$$3x-4=x+14$$

Now, let's solve for $x$:

1. Subtract $x$ from both sides:

$$3x-x-4=14$$

2. This simplifies to:

$$2x-4=14$$

3. Next, add 4 to both sides:

$$2x=18$$

4. Finally, divide by 2:

$$x=9$$

Thus, the value of $x$ is 9.