# How To Construct A Rectangle : 2

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

## Some Solved Examples on how to construct a rectangle

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.

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.

Then, ABCD is the required rectangle

## Some more Solved Examples on how to construct a 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 600 . 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 = 600.

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

Then, ABCD is the required rectangle.