41.9k views
2 votes
Given trapezoid PQRS, find the length of midsegment TU.

Given trapezoid PQRS, find the length of midsegment TU.-example-1

1 Answer

1 vote

Answer:

Option (4)

Explanation:

In the given picture,

Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.

Segment TU joins the midpoints of the sides PS and RQ.

Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."

Therefore, m(TU) =
(1)/(2)(m\text{PQ}+m\text{SR})

7x - 26 =
(1)/(2)[(3x+23)+(9x-3)]

7x - 26 = 6x + 10

7x - 6x = 26 + 10

x = 36

m(TU) = 7x - 26

= 7(36) - 26

= 252 - 26

= 226

Therefore, Option (4) will be the answer.

User Aameer
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories