Question

Use the image to answer the 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 \( \boxed{17} \).