Answer:
- x = 7
- y = 12
- PQ = QR = 29
- PS = SR = 32
- PT = 18
- PR = 36
Explanation:
Based on the markings and the given information, we know PS = SR, PQ = QR, and PT = TR. This lets us write equations to find x and y.
x
PS = SR
4x +4 = 7x -17
21 = 3x . . . . . . . add 17-4x
7 = x . . . . . . . divide by 3
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y
PQ = QR
5y -31 = 2y +5
3y = 36 . . . . . . . . add 31-2y
y = 12 . . . . . . divide by 3
__
Then the segment lengths are ...
PQ = QR = 2(12) +5 = 29
PS = SR = 4(7) +4 = 32
PT = 6(7) -2(12) = 42 -24 = 18
PR = 2×PT = 2(18) = 36