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Question

Parallelogram upper J upper K upper L upper M is shown with base upper L upper M shorter than the height upper L upper K. Diagonals are drawn from upper J to upper L and upper K to upper M to meet at upper N.

In parallelogram JKLM
, diagonals KM
and JL
meet at point N
. The length of KM
is equal to 5x+1
units. The length of NM
is equal to 2x+9
units. What is the value of x?

(1 point)
units

Answer 1

In a parallelogram, the diagonals bisect each other. This means that the length of segment \( KN \) is equal to the length of segment \( NM \). Given the lengths:

• \( KM = 5x + 1 \)
• \( NM = 2x + 9 \)

Since point \( N \) is the midpoint of diagonal \( KM \), we have:

\[ KN = \frac{KM}{2} = \frac{5x + 1}{2} \] and \[ NM = 2x + 9. \]

Since \( KN \) is equal in length to \( NM \):

\[ \frac{5x + 1}{2} = 2x + 9. \]

To eliminate the fraction, we can multiply both sides by 2:

\[ 5x + 1 = 4x + 18. \]

Next, we will isolate \( x \) by subtracting \( 4x \) from both sides:

\[ 5x - 4x + 1 = 18, \] which simplifies to:

\[ x + 1 = 18. \]

Now, subtract 1 from both sides:

\[ x = 17. \]

So, the value of \( x \) is \( \boxed{17} \).