Construct a rectangle PQRS in which QR = 3.6 cm and diagonal PR = 6 cm.


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


Steps of construction:

Step 1: Draw $Q R=3.6 \mathrm{~cm}$

Step 2: Make $\angle Q=90^{\circ}$

$\angle R=90^{\circ}$

Step 3:

$P R^{2}=P Q^{2}+Q R^{2}$

$6^{2}=P Q^{2}+3.6^{2}$

$P Q^{2}=36-12.96$

$P Q^{2}=23.04$

$P Q=4.8 \mathrm{~cm}$

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 and S.

Thus, PQRS is the required rectangle. The other side is 4.8 cm in length.

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