Using the triangle proportionality theorem, the perimeter can be determined as: 114.61 units.
What is the Triangle Proportionality Theorem?
The triangle proportionality theorem states that if a line segment that is parallel to one side of a triangle, joins the other two sides of the triangle, it divides the two sides proportionally.
Thus, find VW using the triangle proportionality theorem:
VW/WX = VZ/ZY
VW/36 = (44 - 27.5)/27.5
VW/36 = 16.5/27.5
VW = 21.6
Find XY using Pythagorean Theorem:
XY = √(VX² - VY²)
XY = √(57.6² - 44²)
XY = 37.17
Find WZ:
WZ/XY = VZ/VY
WZ/37.17 = 16.5/44
WZ = 13.94
Perimeter of Trapezoid WXYZ = WX + XY + YZ + WZ
Perimeter = 36 + 37.17 + 27.5 + 13.94
Perimeter = 114.61 units.
Learn more about triangle proportionality theorem on:
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