25.5k views
5 votes
CD is the mid segment of trapezoid WXYZ.-What is the value of X?-What is XY?-What is WZ?

CD is the mid segment of trapezoid WXYZ.-What is the value of X?-What is XY?-What-example-1

1 Answer

6 votes

The midsegment theorem states that the length of the midsegment is equal to half the length of the base. From the information given,

midsegment = CD = 22

base = XY = 4x + 1

By applying the midsegment theorem, we have

CD = 1/2XY

22 = 1/2(4x + 1)

By crossmultiplying, we have

22 * 2 = 4x + 1

44 = 4x + 1

4x = 44 - 1

4x = 43

x = 43/4

x = 10.75

Thus,

Substituting x = 10.75 into XY = 4x + 1, it becomes

XY = 4(10.75) + 1

XY = 43 + 1

XY = 44

Substituting x = 10.75 into WZ = x + 3, it becomes

WZ = 10.75 + 3

WZ = 13.75

User Tfl
by
6.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.