Given trapezoid MNOP with a median QR, find the value of x
MN=x+2,OP= 3x-10, median 16
[(x+2) + (3x-10)]/2 = 16
x=10
To find the value of x in trapezoid MNOP, we can start by using the properties of a trapezoid and the given information.
In a trapezoid, the median is the line segment connecting the midpoints of the two non-parallel sides. In this case, the median is segment QR.
Let's use the given information to set up an equation for the lengths of the sides MN and OP in terms of x:
MN = x + 2
OP = 3x - 10
Since QR is the median, it should be equal to the average of the lengths of the two non-parallel sides. In other words, QR should be the average of MN and OP:
QR = (MN + OP) / 2
Substituting the values for MN and OP:
16 = (x + 2 + 3x - 10) / 2
Now, we can solve for x.
To do this, multiply both sides of the equation by 2 to eliminate the fraction:
32 = x + 2 + 3x - 10
Combine like terms:
32 = 4x - 8
Next, isolate the variable x by adding 8 to both sides:
32 + 8 = 4x
40 = 4x
Finally, solve for x by dividing both sides by 4:
40 / 4 = x
x = 10
Therefore, the value of x in trapezoid MNOP is 10.