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)
Answers
GPT-4o mini
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**.
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**.