# How To Construct A Rectangle

Introduction

In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle. A rectangle with vertices ABCD would be denoted as ABCD. (Source: Wikipedia)

How to Construct

To construct a rectangle when it’s two adjacent sides. In a properly used rectangle, each angle is a right angle and opposite sides is equal.

## Example problems for how to construct a rectangle

Problem 1:-

Construct a rectangle ABCD in which AB = 5 cm and BC = 4 cm. How to construct?

Steps for Construct

Step1:-  Draw a line segment AB of length 5 cm.

Step2:-  At B, draw BE AB.

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

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

Step5:-  With C as centre position ad radius 5 cm draws another arc cutting the previous arc at D.

Step6:-  Join AD and CD. Then, ABCD is the required rectangle.

Construct

To construct a rectangle with one diagonal and one side are given.

Problem 2:-

To Construct a rectangle ABCD in the given sides AB = 4 cm, and diagonal AC = 5 cm. How to construct?

Steps for Construct

Step1:- Draw al line segment AB of length 4 cm.

Step2:- At B, draw BE AB.

Step3:- With A as centre position 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:- With centre position 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.

## More Example problem for how to construct a rectangle

Problem 1:-

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

Let diagonal AC = 6.4 cm and the angle between the two diagonals be 600.How to construct?

Steps for Construct

Step1:- Draw AC = 6.4 cm.

Step2:- Draw the perpendicular bisector of AC and find the mid-point of AC. Let the perpendicular.Bisectors 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.