Construct a quadrilateral PQRS in which QR = 7.5 cm,
Question:

Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS = 10 cm. Measure the fourth side.

Solution:

Steps of construction:

Step 1: Draw $Q R=7.5 \mathrm{~cm}$.

Step 2: With $Q$ as the centre and radius equal to $10 \mathrm{~cm}$, draw an arc.

Step 3: With $R$ as the centre and radius equal to $5 \mathrm{~cm}$, draw another arc, cutting the previous arc at $S$. Step 4: Join $Q S$ and $R S$.

Step 5: With $S$ as the centre and radius equal to $6 \mathrm{~cm}$, draw an arc.

Step 6: With $R$ as the centre and radius equal to $6 \mathrm{~cm}$, draw another arc, cutting the previous arc at $P$.

Step 7: Join $P S$ and $P R$.

Step 8: $P Q=4.9 \mathrm{~cm}$

Thus, PQRS is the required quadrilateral.