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?

Answer 1

In a parallelogram, the diagonals bisect each other. Therefore, the length of diagonal KM is twice the length of segment NM.

Let’s denote the lengths mathematically. We have:

- Length of \( KM = 5x + 1 \)
- Length of \( NM = 2x + 9 \)

Since N is the midpoint of KM, we have:

\[
NM = \frac{1}{2} KM
\]

Substituting the expressions for \( KM \) and \( NM \) into the equation gives:

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

To eliminate the fraction, multiply both sides by 2:

\[
2(2x + 9) = 5x + 1
\]

Distributing on the left side:

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

Now, let’s solve for \( x \). First, subtract \( 4x \) from both sides:

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

This simplifies to:

\[
18 = x + 1
\]

Now, subtract 1 from both sides:

\[
17 = x
\]

Thus, the value of \( x \) is:

\[
\boxed{17}
\]