Parallelogram LMNO has two diagonal lines, LN and MO, that intersect at P. The length of LP can be expressed by 3x4, 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 length of the segments created by the diagonals is equal on both sides of the intersection point.

Given:

• \( LP = 3x + 4 \)
• \( PN = x + 14 \)

Since \( P \) is the midpoint of both diagonals \( LN \) and \( MO \), we have:

\[ LP = PN \]

So we can set up the equation:

\[ 3x + 4 = x + 14 \]

Now, let's solve for \( x \).

1. Subtract \( x \) from both sides:

\[ 3x - x + 4 = 14 \]

This simplifies to:

\[ 2x + 4 = 14 \]

2. Next, subtract 4 from both sides:

\[ 2x = 14 - 4 \]

This gives us:

\[ 2x = 10 \]

3. Divide both sides by 2:

\[ x = 5 \]

Thus, the value of \( x \) is \( \boxed{5} \).