Question

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**.