Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 4 Practical Geometry Ex 4.5 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 8 Maths Chapter 4 Practical Geometry Ex 4.5

Draw the following.

Question 1.

The square READ with RE = 5.1 cm.

Solution:

Steps of construction :

- Draw a line segment RE = 5.1 cm.
- At E, draw \(\overrightarrow{\mathrm{EM}}\), such that ∠REM = 90°.
- With E as centre and radius =5.1 cm, draw an arc intersecting \(\overrightarrow{\mathrm{EM}}\) at A.
- With R as centre and radius = 5.1 cm, draw an arc.
- With A as centre and radius = 5.1 cm, draw an arc which intersect the previous arc at D.
- Draw \(\overline{\mathrm{RD}}\) and \(\overline{\mathrm{AD}}\).

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 angle.]

Here, in rhombus XYZW, YW 6.4 cm.

∴ OW = OY = 3.2 cm

Steps of construction:

- Draw a line segment XZ = 5.2 cm.
- Draw \(\overleftrightarrow{\mathrm{AB}}\), the perpendicular bisector of \(\overline{\mathrm{XZ}}\), which intersect \(\overline{\mathrm{XZ}}\) at O.
- With O as centre and radius = 3.2 cm, draw an arc intersecting \(\overleftrightarrow{\mathrm{AB}}\) above \(\overline{\mathrm{XZ}}\) at W.
- With O as centre and radius = 3.2 cm, draw another arc which intersects \(\overleftrightarrow{\mathrm{AB}}\) below \(\overline{\mathrm{XZ}}\) at Y.
- Draw \(\overline{\mathrm{XY}}\), \(\overline{\mathrm{YZ}}\), \(\overline{\mathrm{ZW}}\) and \(\overline{\mathrm{XW}}\).

Thus, XYZW is the required rhombus.

Question 3.

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

Solution:

[Note: Each angle of a rectangle is a right angle.]

Steps of construction :

- Draw a line segment AB = 5 cm.
- At A, draw \(\overrightarrow{\mathrm{AX}}\), such that ∠XAB = 90°.
- With A as centre and radius = 4 cm, draw an arc intersecting \(\overrightarrow{\mathrm{AX}}\) at D.
- With B as centre and radius = 4 cm, draw an arc.
- With D as centre and radius = 5 cm, draw an arc which intersects the previous arc at C.
- Draw \(\overline{\mathrm{BC}}\) and \(\overline{\mathrm{CD}}\).

Thus, ABCD is the required rectangle.

Question 4.

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

Solution:

A parallelogram cannot be constructed as sufficient measurements are not given. It is not unique as angles may vary in parallelogram drawn by given measurements.