Question

example 2
trapezoid rhwa with midsegment (overline{uk}) is shown. find the values of(x) and (y) if (ru = -2x - 2y), (au = 10), (rh = 4x), (uk = 14), and (aw = x + 13)

example 3
located on the nature coast state trail in north - central florida is the suwannee river trestle, a bridge that is shaped like an isosceles trapezoid. the state has been inspecting older bridges to ensure their safety and has determined that the suwannee river trestle, represented as trapezoid zymu, needs an additional support brace through its middle.
the support brace is to connect sides (overline{zu}) and (overline{ym}) at their midpoints. if the length of leg (zu = 2) feet (ft) and the perimeter of the trestle measures 153 ft, what is the length, in ft, of the new support brace?

Explanation:

Step1: Note isosceles trapezoid properties

The legs $ZU = YM = 21$ ft (equal legs in isosceles trapezoid).

Step2: Calculate sum of the two bases

Let the two bases be $ZY$ and $UM$. Perimeter $P = ZY + UM + ZU + YM$.
$153 = (ZY + UM) + 21 + 21$
$ZY + UM = 153 - 42 = 111$

Step3: Apply midsegment theorem

The support brace is the midsegment of the trapezoid, so its length is $\frac{ZY + UM}{2}$.
$\text{Length} = \frac{111}{2} = 55.5$

Answer:

55.5 ft