## MP Board Class 8th Maths Solutions Chapter 4 Practical Geometry Ex 4.5

Question 1.

Draw the following.

(i) The square READ with RE = 5.1 cm.

(ii) A rhombus whose diagonals are 5.2 cm and 6.4 cm long.

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

(iv) A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm.

Solution:

(i) Since, all 4 sides of a square are equal and each of 4 angles is equal to 90°.

Steps of Construction:

Step-1: Draw RE = 5.1 cm.

Step-2 : Draw ∠REX = 90°.

Step-3 : Cut off EA = 5.1 cm on \(\overrightarrow{E X}\)

Step-4: With R as centre and radius equal to 5.1 cm, draw an arc.

Step-5 : With A as centre and radius equal to 5.1 cm, cut off another arc on the arc drawn in step-4 at point D.

Step-6 : Join DA and DR.

Hence, READ is the required square.

(ii) We know that diagonals of a rhombus bisect each other at right angles. Let AC = 5.2 cm and BD = 6.4 cm.

Steps of Construction:

Step-1: Draw AC = 5.2 cm.

Step-2 : Draw perpendicular bisector XY of AC which cut AC at point O.

Step-3 : Cut off OD = 3.2 cm on OX and OB = 3.2 cm on \(\overrightarrow{O Y}\).

Step-4 : Join AD, CD, AB and CB.

Hence, ABCD is the required rhombus.

(iii) In a rectangle, opposite sides are equal and each of 4 angles is equal to 90°.

Let AB = 5 cm and BC = 4 cm

∴ AB = DC = 5 cm and BC = AD = 4 cm.

Also, ∠A = ∠B = ∠C = ∠D = 90°.

Steps of Construction:

Step-1: Draw AB = 5 cm.

Step-2 : Draw ∠ABX = 90°.

Step-3 : Cut off BC = 4 cm on BX .

Step-4: With A as centre and radius equal to 4 cm, cut off an arc.

Step-5 : With C as centre and radius equal to 5 cm cut off another arc on the arc drawn in step-4 at point D.

Step-6 : Join AD and CD.

Hence, ABCD is the required rectangle.

(iv) Here, data given is incomplete. Since we know that to draw a quadrilateral at least five parts are necessary. In the present case, OK = 5.5 cm & KA = 4.2 cm is given.

We know that opposite sides of a parallelogram are equal.

∴ OK = YA = 5.5 cm and KA = OY = 4.2 cm

Here, only four parts are given. This means that one more part is necessary.

So, either one angle or diagonal of a parallelogram is required to construct it.

Hence, parallelogram OKAY cannot be drawn.