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.