Question
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)
Answers
GPT-4o mini
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 \( \boxed{5} \).
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 \( \boxed{5} \).