RD Sharma solution class 8 chapter 18 Practical Geometry(constructions) Exercise 18.2

Exercise 18.2

Page-18.6

Question 1:

Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3.0 cm, AD = 2.3 cm, AC = 4.5 cm and BD = 3.8 cm.

Answer 1:

$$\begin{gathered} \mathrm{Steps} \mathrm{o}f \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AC}=6 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.8 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.0 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{II} \mathrm{at} \mathrm{B}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.8 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{on} \mathrm{the} \mathrm{other} \mathrm{side} \mathrm{of} \mathrm{AC}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 2.3 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{D}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{BA}, \mathrm{DA}, \mathrm{BC} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 2:

Construct a quadrilateral ABCD in which BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD = 10 cm.

Answer 2:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AC}=6 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 6 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{II} \mathrm{at} \mathrm{D}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 10 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{on} \mathrm{the} \mathrm{other} \mathrm{side} \mathrm{of} \mathrm{the} \mathrm{line} \mathrm{segment} \mathrm{AC}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 7.5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{B}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{BA}, \mathrm{DA}, \mathrm{BC} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 3:

Construct a quadrilateral ABCD, when AB = 3 cm, CD = 3 cm, DA = 7.5 cm, AC = 8 cm and BD = 4 cm.

Answer 3:

If we consider a triangle ABD from the given data, then
AB = 3 cm
BD = 4 cm
AD = 7.5 cm
AB + BD = 3 + 4 = 7 cm
However, we know that the sum of the lengths of two sides of a triangle is always greater than the third side.
Therefore, construction is not possible from the given data.

Question 4:

Construct a quadrilateral ABCD given AD = 3.5 cm, BC = 2.5 cm, CD = 4.1 cm, AC = 7.3 cm and BD = 3.2 cm.

Answer 4:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{CD}=4.1 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 7.3 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{II} \mathrm{at} \mathrm{A}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.2 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{on} \mathrm{the} \mathrm{other} \mathrm{side} \mathrm{of} \mathrm{AC}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 2.5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{B}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{BA}, \mathrm{DA}, \mathrm{BC} \mathrm{and} \mathrm{B}D \mathrm{and} \mathrm{AC} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 5:

Construct a quadrilateral ABCD given AD = 5 cm, AB = 5.5 cm, BC = 2.5 cm, AC = 7.1 cm and BD = 8 cm.

Answer 5:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=5.5 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 7.1 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 2.5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{II} \mathrm{at} \mathrm{C}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 8 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{D}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{DA}, \mathrm{DB}, \mathrm{BC}, \mathrm{AC} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 6:

Construct a quadrilateral ABCD in which BC = 4 cm, CA = 5.6 cm, AD = 4.5 cm, CD = 5 cm and BD = 6.5 cm.

Answer 6:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{BC}=4 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 6.5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{II} \mathrm{at} \mathrm{D}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5.6 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{on} \mathrm{the} \mathrm{same} \mathrm{side}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4.5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{A}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{BA}, \mathrm{AC}, \mathrm{DA}, \mathrm{BD} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$