Answer:
<h2>QT = 21</h2><h2>SV = 41</h2>
Step-by-step explanation:
From the diagram, it can be seen that TR is parallel to RV. This means that TR = RV. Given TR = 17 and RV = 3x+2
3x+2 = 17
3x = 17-2
3x = 15
x = 5
RV = 3(5)+2 = 17
QV = 4x+1 = 4(5)+1
QV = 21
Using Pythagoras theorem on ΔQRV to get RQ
QV² = QR²+RV²
21² = QR²+17²
QR² = 21²-17²
QR = 12.33
Using Pythagoras theorem on ΔQRT to get QT
From ΔQRT,
QT² = QR²+TR²
QT² = 12.33²+17²
QR² = 152.0289+289
QT² = 441.0289
QT =21
Since TS = 9(5)-4 = 41
Using Pythagoras theorem on ΔTRS
From ΔTRS,
TS² = RS²+TR²
41² = RS²+17²
RS² = 41²-17²
RS² = 1392
RS = 37.31
Similarly Using Pythagoras theorem on ΔRSV
From ΔRSV,
SV² = RV²+RS²
SV² = 17²+37.31²
SV² = 1681.0361
SV = 41
