Question

use the image to answer the 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

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, \(KM = 2\times NM\).
Given \(KM=5x + 1\) and \(NM = 2x+9\), we substitute into the equation:
\(5x + 1=2(2x + 9)\)

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b=2x\), \(c = 9\)), we get:
\(5x+1 = 4x+18\)

Step3: Solve for \(x\)

Subtract \(4x\) from both sides of the equation:
\(5x-4x+1=4x - 4x+18\)
\(x+1=18\)
Then subtract \(1\) from both sides:
\(x+1 - 1=18 - 1\)

Answer:

\(x = 17\)