Question

Construct a rectangle PQRS in which QR = 3.6 cm and diagonal PR = 6 cm. Measure the other side of the rectangle.

Answer 1

Steps of construction:
Step 1: Draw QR = $3.6cm$
Step 2: Make $$\begin{gathered} \angle Q={90}^{\circ } \\ \angle R={90}^{\circ } \end{gathered}$$
Step 3:
$$\begin{gathered} P{R}^2=P{Q}^2+Q{R}^2 \\ {6}^2=P{Q}^2+3.6^2 \\ P{Q}^2=36-12.96 \\ P{Q}^2=23.04 \\ PQ=4.8\mathrm{cm} \end{gathered}$$

Step 3: Draw an arc of length 4.8 cm from point Q and name that point as P.
​Step 4: Draw an arc of length 6 cm from point R, cutting the previous arc at P.
​Step 5: Join PQ
Step 6: Draw an arc of length 4.8 cm from point R.
From point P, draw an arc of length 3.6 cm, cutting the previous arc. Name that point as S.
Step 7: Join P and S.
Thus, PQRS is the required rectangle. The other side is 4.8 cm in length.