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)

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, $KM = 2\times NM$.

Step2: Set up the equation

Substitute the given expressions for $KM$ and $NM$ into the equation: $5x + 1=2(2x + 9)$.

Step3: Expand the right - hand side

Using the distributive property $a(b + c)=ab+ac$, we get $5x + 1 = 4x+18$.

Step4: Solve for $x$

Subtract $4x$ from both sides: $5x-4x + 1=4x-4x + 18$, which simplifies to $x+1 = 18$. Then subtract 1 from both sides: $x=18 - 1$.

Answer:

$x = 17$