**Construction**

** **To construct a rectangle when its tow adjacent sides are given

**Property Used**

In a rectangle, each angle is a right angle and opposite sides are equal

**Ex 1 : ** Construct a rectangle ABCD in which AB = 5 cm and BC = 4 cm

**Sol : Steps Of Construction**

** **Step1. Draw a line segment AB of length 5 cm

Step2. At B, draw BE │ AB.

Step3. With B as centre and radius 4 cm, draw an arc, cutting BE at C.

Step4. With A as centre and radius 4 cm, draw an arc

Step5. With C as centre ad radius 5 cm, draw another arc, cutting the previous arc at D.

Step6. Join AD and CD

Then, ABCD is the required rectangle.

**Construction**

To construct a rectangle whose one diagonal and one side are given

**Ex 2 : ** Construct a rectangle ABCD in which side AB = 4 cm, and diagonal AC = 5 cm.

**Sol : Steps Of Construction**

Step1. Draw al line segment AB of length 4 cm

Step2. At B, draw BE │ AB

Step3. With A as centre and radius 5 cm, draw an arc cutting BE at C.

Step4. With centre B and radius equal to AC = 5 cm, draw an arc

Step5. Wit centre C and radius equal to AB = 4 cm, another arc, cutting the previous arc at D.

Step6. Join AD and CD

Then, ABCD is the required rectangle

**Example**

When one diagonal AC = 6.4 cm and the angle between the two diagonals are given

**Q:** A rectangle have diagonal AC = 6.4 cm and the angle between the two diagonals be 60^{0} . Consturct the rectangle

**Sol:** Step1. Draw AC = 6.4 cm

Step2. Draw the perpendicular bisector of AC to locate the mid-point of AC. Let the perpendicular

bisector intersect AC at point O.

Step3. Through O, construct a line POQ so that angle POC = 60^{0}.

Step4. From OP cut OD equal to OC (i.e. 3·2cm) and from OQ

Then, ABCD is the required rectangle.