These NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.5 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.5

Draw the following.

Question 1.

The square READ with RE = 5.1 cm.

Solution:

Steps of construction:

I. Draw a line segment RE = 5.1 cm.

II. At E, draw \(\overrightarrow{\mathrm{EX}}\), such that ∠REX = 90°.

III. From \(\overrightarrow{\mathrm{EX}}\), cut-off \(\overrightarrow{\mathrm{EA}}\) = 5.1 cm.

IV. With centre at A, draw an arc above RE of radius = 5.1 cm.

V. With centre at R, and radius = 5.1 cm, draw another arc to intersect the previous arc at D.

VI. Join DA and DR. Thus, READ is the required square.

Question 2.

A rhombus whose diagonals are 5.2 cm and 6.4 cm long.

Solution:

Note: The diagonals of a rhombus bisect each other at right angles.

Steps of Construction:

I. Draw a line segment AC = 5.2 cm.

II. Draw \(\overrightarrow{\mathrm{XY}}\), the perpendicular bisector of AC.

III. From XY, cut-off OD = \(\frac{1}{2}\) × (6.4 cm) = 3.2 cm.

IV. Similarly, cut-off OB = \(\frac{1}{2}\) × (6.4 cm) = 3.2 cm.

V. Join AD, DC, CB, and BA. Thus, ABCD is the required rhombus.

Question 3.

A rectangle with adjacent sides of length 5 cm and 4 cm.

Solution:

Steps of Construction:

I. Draw a line segment PQ = 5 cm

II. At Q draw \(\overrightarrow{\mathrm{QX}}\) such that ∠PQX = 90°

III. From \(\overrightarrow{\mathrm{QX}}\), cut-off QR = 4 cm.

IV. With centre R and radius = 5 cm draw an arc.

V. With centre P and radius = 4 cm draw an arc to intersect the previous arc at S.

VI. Join RQ and RS. Thus, PQRS is the required rectangle.

Question 4.

A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

Solution:

Steps of Construction:

I. Draw a line segment OK = 5.5 cm.

II. At K, draw a ray \(\overrightarrow{\mathrm{KX}}\).

III. From \(\overrightarrow{\mathrm{KX}}\), cut-off KA = 4.2 cm.

IV. With centre at A and radius = 5.5 cm draw an arc above OK.

V. With centre O and radius = 4.2 cm, draw another arc to intersect the previous arc at Y.

VI. Join OY and AY. Thus, OKAY is the required parallelogram.