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Given △VXY and △VWZ, what is the perimeter of the trapezoid WXYZ? Round your answer to the nearest hundredth.


Triangle VXY with Segment WZ parallel to XY

Sagot :

akposevictor

The perimeter of trapezoid WXYZ, to the nearest hundredth, is: 195.00 units.

What is the Perimeter of a Shape?

Perimeter of a shape is the sum of all the sides of the shape.

Perimeter of trapezoid WXYZ = WX + XY + YZ + ZW

  • YZ = 50
  • WX = 62.5

Find XY and ZW.

Since △VXY and △VWZ are similar triangles, therefore:

VY/VZ = VX/VW

VY = 80

VZ = 80 - 50 = 30

VX = 62.5 + VW

VW = ?

Substitute

80/30 = (62.5 + VW)/VW

Cross multiply

80VW = 30(62.5 + VW)

80VW = 1,875 + 30VW

80VW - 30VW = 1,875

50VW = 1,875

VW = 1,875/50

VW = 37.5

Using Pythagorean theorem, find ZW:

ZW = √(VW² - VZ²)

Substitute

ZW = √(37.5² - 30²)

ZW = 22.5

Find XY:

XY/ZW = VY/VZ

XY/22.5 = 80/30

XY = (80 × 22.5)/30

XY = 60

Perimeter of trapezoid WXYZ = WX + XY + YZ + ZW

= 62.5 + 60 + 50 + 22.5

= 195.00 units.

Learn  more about perimeter of a shape on:

https://brainly.com/question/16542774

View image akposevictor
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