Excercise 4.5 Practical Geometry- NCERT Solutions Class 8

Go back to  'Practical Geometry'

Chapter 4 Ex.4.5 Question 1

Draw the following:

1. A square \(READ\) with \(RE = 5.1\,\rm{cm.}\)

2. A rhombus whose diagonals are \(5.2\,\rm{cm}\) and \(6.4\,\rm{cm}\) long.

3. A rectangle with adjacent sides of lengths \(5\,\rm{cm}\) and \(4\,\rm{cm.}\)

4. A parallelogram \(OKAY\) where \(OK = 5.5\,\rm{cm} \) and \(KA = 4.2\,\rm{cm.}\) Is it unique?

Solution

Video Solution

What is the known?

Diagonals of a Rhombus.

What is unknown?

Construction of a Rhombus

Reasoning:

We need five measurements to draw a unique quadrilateral.

But we also know that diagonals of rhombus bisect each other at right angles and all sides of rhombus are equal. We can use this information to construct the rhombus.

Steps:

Step 1: Draw a line segment \(AB=6.4\,\rm{cm.}\)

Step 2: Draw perpendicular bisector of \(AB\) meeting \(AB\) at \(O.\)

Step 3: \(5.2\,\rm{cm}\) divided by \(2 = 2.6 \,\rm{cm.}\) Measure \(2.6\,\rm{cm}\) from \(O\) on either side of \(AB\) on perpendicular bisector and mark them as \(C\) and \(D.\)

Step 4: Join \(AC, AD, BC\) and \(BD.\)

Step 5: \(ABCD\) is the required rhombus.

Related Problems:

(1) The square \(READ\) with \(RE=5.1\,\rm{cm}\)

Hint: All sides of square are equal, and angles are at right angles.

(2) A rectangle with adjacent sides of lengths \(5\,\rm{cm}\) and \(4\,\rm{cm.}\)

Hint: Opposite sides of rectangle are equal and parallel, and angles are at right angles.

(3) A parallelogram \(OKAY\) where \(OK=5.5\,\rm{cm}\) and \(KA=4.2\,\rm{cm.}\)

Hint: Opposite sides of a parallelogram are parallel and equal. Using this information, parallelogram can be constructed with a convenient angle.

  
Download Cuemath NCERT App
Related Sections
Related Sections

Learn from the best math teachers and top your exams

Learn from the best

math teachers and top

your exams


Personalized Curriculum
Instant Doubts clarification
Cover latest CBSE Syllabus
Unlimited Mock & Practice tests
Covers CBSE, ICSE, IB curriculum

Instant doubt clearing with Cuemath Advanced Math Program
0