Answer:
B. QT = 18; TR = 8
Step-by-step explanation:
QT = x + 6
SR = 12
PS = 27
TR = x - 4
PR/SR = QR/TR (Similarity theorem)
PR = PS + SR = 27 + 12
PR = 39
QR = QT + TR = x + 6 + x - 4
QR = 2x + 2
Substitute
39/12 = (2x + 2)/(x - 4)
13/4 = (2x + 2)/(x - 4)
Cross multiply
13(x - 4) = 4(2x + 2)
13x - 52 = 8x + 8
Collect like terms
13x - 8x = 52 + 8
5x = 60
x = 60/5
x = 12
✔️QT = x + 6
Plug in the value of x
QT = 12 + 6
QT = 18
✔️TR = x - 4 = 12 - 4
TR = 8
