Question

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 diagonal KM is divided into two equal segments, which are KN and NM.

Given:
- KM = 5x + 1
- NM = 2x + 9

Since N is the midpoint of KM, we have:
\[ KN = NM \]

Thus, we can set up the equation:
\[
\frac{KM}{2} = NM
\]

This can be rewritten as:
\[
\frac{5x + 1}{2} = 2x + 9
\]

To eliminate the fraction, multiply both sides by 2:
\[
5x + 1 = 4x + 18
\]

Now, isolate x by subtracting 4x from both sides:
\[
5x - 4x + 1 = 18
\]

This simplifies to:
\[
x + 1 = 18
\]

Subtract 1 from both sides:
\[
x = 17
\]

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