In quadrilateral QRTS, we have QR = 11, QS = 9, and ST=2. Sides line RQ and line ST are extended past Q and S, respectively, to meet at point P. If PS = 8 and PQ = 5, then what is RT?
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To find the length of RT, we will use the property that in a quadrilateral, the opposite sides are equal.
Given:
QR = 11
QS = 9
ST = 2
PS = 8
PQ = 5
To find RT, we can first find the length of PS and ST.
Since PQ is extended beyond Q to meet at point P, we can add PQ and QS together to find PS.
PS = PQ + QS = 5 + 9 = 14
Similarly, since PS is extended beyond S to meet at point P, we can subtract ST from PS to find PT.
PT = PS - ST = 14 - 2 = 12
Now, to find RT, we need to find the length of PT and QR.
Since PT is extended beyond T to meet at point P, we can subtract PQ from PT to find RT.
RT = PT - PQ = 12 - 5 = 7
Therefore, RT = 7.