Question

The triangles shown below are similar. Find the length of QS.

Answer 1

Answer: The value of QS is 8 cm.

Explanation:

First calculating the side QT.

As per given figure:

ΔPQT ≈ ΔRST

`(PQ)/(RS)=(QT)/(ST)`

Given:

PQ = 9 cm

RS = 3 cm

ST = 4 cm

Now putting all the given values in the above expression, we get:

`(PQ)/(RS)=(QT)/(ST)\\\\(9cm)/(3cm)=(QT)/(4cm)\\\\QT=12cm`

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.