Class 8 NCERT Solutions – Chapter 4 Practical Geometry – Exercise 4.5

Question 1: Draw the following.
1. The square READ with RE = 5.1 cm.
2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.
4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

Solution:

1. The square READ with RE = 5.1 cm.

Steps of construction:

Step 1: Draw one side of the square RE = 5.1 cm.

Step 2: From E draw an angle of 90°.

Step 3: From E cut EA of 5.1 cm.

Step 4: Now draw an arc of 5.1 cm from both A and R, intersect them and mark the intersection point as D.

Step 5: Join RD and ED.

Thus, we have the required square READ.

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

Steps of construction:

Let the rhombus be ABCD with diagonals, AC = 5.2 cm and BD = 6.4 cm.

Step 1: Draw a line AC of 5.2 cm

Step 2: Draw perpendicular bisector of AC and mark the bisector point as O

Step 3: Draw two arcs with centre O of radius 1/2 × BD = 1/2 × 6.4 cm = 3.2 cm and these arcs will meet the bisector at point B and D    

Step 4: Join AB, BC, CD and AD.

Hence, we have the required rhombus ABCD.

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

Steps of construction:

Step 1: Let the rectangle be CODE with adjacent sides CO = 5 cm and OD = 4 cm.

Step 2: Draw CO = 5 cm.

Step 3: From O draw an angle of 90°.

Step 4: From O cut OD = 4 cm.

Step 5: From C draw an arc of 4 cm and from D draw an arc of 5 cm, intersect both the arcs and mark the point as E.

Step 6: Join CE and DE.

Thus, we have the required rectangle CODE.

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

Steps of construction:

Step 1: Draw a line OK of 5.5 cm.

Step 2: Draw a ray at K at any convenient angle, let the angle be 60°.

Step 3: Now cut the ray at 4.2 cm and mark the point as A.

Step 4: From A draw an arc of 5.5 cm and from O draw an arc of 4.2 cm, intersect both the arcs at Y.

Step 5: Join OY and AY.

Thus, we have the required parallelogram OKAY.
No, it is not unique as angle K can be any angle.