Answer: The value of QS is 8 cm.
Step-by-step explanation:
First calculating the side QT.
As per given figure:
ΔPQT ≈ ΔRST
[tex]\frac{PQ}{RS}=\frac{QT}{ST}[/tex]
Given:
PQ = 9 cm
RS = 3 cm
ST = 4 cm
Now putting all the given values in the above expression, we get:
[tex]\frac{PQ}{RS}=\frac{QT}{ST}\\\\\frac{9cm}{3cm}=\frac{QT}{4cm}\\\\QT=12cm[/tex]
Now calculating the value of QS.
QT = QS + ST
12 cm = QS + 4 cm
QS = 12 cm - 4 cm
QS = 8 cm
Thus, the value of QS is 8 cm.
