Answer:
Using the charasteristics of a parallelogram, the length of line segment MX is 8 in (Third option).
Step-by-step explanation:
In parallelogram WXYZ:
WY=12 in., this is a diagonal in the parallelogram
XZ=16 in., this is the other diagonal in the parallelogram
WX=10 in., this is one of the sides of the parallelogram
XY=9 in., this is the other side of the parallelogram
MX=? this segment is between the vertex X and the point of intersection of the diagonals
In a parallelogram the diagonals intersect (point M) dividing them in equal parts each other, then:
MX=MZ=XZ/2
MX=MZ=(16 in.)/2
MX=MZ=8 in.
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Work Shown:
Length = L = WX = 4x+10
Height = H = XY = 2x-6
P = Perimeter of rectangle = 116
P = 2*(L+H)
2(L+H) = 116
2(4x+10+2x-6) = 116
2(6x+4) = 116
6x+4 = 116/2
6x+4 = 58
6x = 58-4
6x = 54
x = 54/6
x = 9
Using this x value, we find that,
WX = 4x+10 = 4*9+10 = 36+10 = 46
We can also see that
XY = 2x-6 = 2*9-6 = 18-6 = 12
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The length and height of this rectangle are L = 46 and H = 12
This leads to the perimeter of...
P = 2*(L+H)
P = 2*(46+12)
P = 2*(58)
P = 116
This confirms the answer.
