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?
Since KM and NM are diagonals of parallelogram JKLM, they divide each other into two equal parts. Therefore, we have:
5x + 1 = 2(2x + 9)
Simplifying the equation:
5x + 1 = 4x + 18
Subtracting 4x from both sides:
x + 1 = 18
Subtracting 1 from both sides:
x = 17
To find the value of x, we can set up an equation using the given information.
In a parallelogram, the diagonals bisect each other. This means that the length of KM is equal to the length of JL.
So, we can set up the equation: 5x+1 = 2x+9
Now, let's solve for x:
Subtract 2x from both sides: 5x+1-2x = 2x+9-2x
This simplifies to: 3x+1 = 9
Subtract 1 from both sides: 3x+1-1 = 9-1
This simplifies to: 3x = 8
Finally, divide both sides by 3: (3x)/3 = 8/3
This gives us the value of x: x = 8/3
So, the value of x is 8/3.
To find the value of x, we can use the fact that diagonals of a parallelogram bisect each other. This means that the lengths of KM and JL are equal.
Let's set up an equation to represent this:
5x + 1 = 2x + 9
To solve for x, we need to isolate the variable on one side of the equation.
First, we can move the 2x term to the left side:
5x - 2x + 1 = 9
This simplifies to:
3x + 1 = 9
Next, we can move the constant term to the right side:
3x = 9 - 1
Simplifying further:
3x = 8
Finally, we can solve for x by dividing both sides of the equation by 3:
x = 8 / 3
Therefore, the value of x is 8/3.