RD Sharma solution class 8 chapter 18 Practical Geometry(constructions) Exercise 18.3

Exercise 18.3

Page-18.8

Question 1:

Construct a quadrilateral ABCD in which AB = 3.8 cm, BC = 3.4 cm, CD = 4.5 cm, AD = 5 cm and ∠B = 80°.

Answer 1:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=3.8 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{ABC}=80°. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.4 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BC}=3.4 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 4.5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5.3 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{D}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} AD, \mathrm{BC} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 2:

Construct a quadrilateral ABCD, given that AB = 8 cm, BC = 8 cm, CD = 10 cm, AD = 10 cm and ∠A = 45°.

Answer 2:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{Construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=8 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{BAD}=45°. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 10 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{AD}=10 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 10 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 8 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{C}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{BC} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 3:

Construct a quadrilateral ABCD in which AB = 7.7 cm, BC = 6.8 cm, CD = 5.1 cm, AD = 3.6 cm and ∠C = 120°.

Answer 3:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{DC}=5.1 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{DCB}=120°. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 6.8 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BC}=6.8 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 7.7 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.6 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{A}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} AB \mathrm{and} AD \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 4:

Construct a quadrilateral ABCD in which AB = BC = 3 cm, AD = CD = 5 cm, and ∠B = 120°.

Answer 4:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=3 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{ABC}=120°. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BC}=3 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{C} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 5 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{D}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{AD} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 5:

Construct a quadrilateral ABCD in which AB = 2.8 cm, BC = 3.1 cm, CD = 2.6 cm, and DA = 3.3 cm and ∠A = 60°.

Answer 5:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=2.8 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{BAD}=60°. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{A} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.3 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{AD}=3.3 \mathrm{cm}. \\ \mathrm{Step} \mathrm{IV}: \mathrm{With} \mathrm{D} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 2.6 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc}. \\ \mathrm{Step} V :\mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 3.1 \mathrm{cm}, \mathrm{draw} \mathrm{an} \mathrm{arc} \mathrm{to} \mathrm{intersect} \mathrm{the} \mathrm{arc} \mathrm{drawn} \mathrm{in} \mathrm{Step} \mathrm{IV} \mathrm{at} \mathrm{C}. \\ \mathrm{Step} \mathrm{VI}: \mathrm{Join} \mathrm{BC} \mathrm{and} \mathrm{CD} \mathrm{to} \mathrm{obtained} \mathrm{the} \mathrm{required} \mathrm{quadrilateral}. \end{gathered}$$

Question 6:

Construct a quadrilateral ABCD in which AB = BC = 6 cm, AD = DC = 4.5 cm and ∠B = 120°.

Answer 6:

$$\begin{gathered} \mathrm{Steps} \mathrm{of} \mathrm{construction}: \\ \mathrm{Step} \mathrm{I}: \mathrm{Draw} \mathrm{AB}=6 \mathrm{cm}. \\ \mathrm{Step} \mathrm{II}: \mathrm{Construct} \angle \mathrm{ABC}=120°. \\ \mathrm{Step} \mathrm{III} : \mathrm{With} \mathrm{B} \mathrm{as} \mathrm{the} \mathrm{centre} \mathrm{and} \mathrm{radius} 6 \mathrm{cm}, \mathrm{cut} \mathrm{off} \mathrm{BC}=6 \mathrm{cm}. \\ \mathrm{Now}, \mathrm{we} \mathrm{can} \mathrm{see} \mathrm{that} \mathrm{AC} \mathrm{is} \mathrm{about} 10.3 \mathrm{cm} \mathrm{which} \mathrm{is} \mathrm{greater} \mathrm{than} \mathrm{AD}+\mathrm{CD}=4.5+4.5=9 \mathrm{cm}. \\ \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{sum} \mathrm{of} \mathrm{the} \mathrm{lengths} \mathrm{of} \mathrm{two} \mathrm{sides} \mathrm{of} \mathrm{triangle} \mathrm{is} \mathrm{always} \mathrm{greater} \mathrm{than} \mathrm{the} \mathrm{third} \mathrm{side} \mathrm{but} \mathrm{here}, \mathrm{the} \mathrm{sum} \mathrm{of} \mathrm{AD} \mathrm{and} \mathrm{CD} \mathrm{is} \mathrm{less} \mathrm{than} \mathrm{AC}. \\ \mathrm{So}, \mathrm{construction} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{quadrilateral} \mathrm{is} \mathrm{not} \mathrm{possible}. \end{gathered}$$