**NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry Exercise 4.2**

Ex 4.2 Class 8 Maths Question 1.

Construct the following quadrilaterals.

(i) Quadrilateral LIFT

LI = 4 cm

IF = 3 cm

TL = 2.5 cm

LF = 4.5 cm

IT = 4 cm

(ii) Quadrilateral GOLD

OL = 7.5 cm

GL = 6 cm

GD = 6 cm

LD = 5 cm

OD = 10 cm

(iii) Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

Solution:

(i) Construction:

StepI: Draw LI = 4 cm.

Step II: Draw an arc with centre I and radius 3 cm.

StepIII: Draw another arc with centre L and radius 4.5 cm to meet the former arc at F.

Step IV: Join LF and IF.

StepV: Draw an arc with centre L and radius 2.5 cm.

Step VI: Draw another arc with centre I and radius 4 cm to meet the previous arc at T.

StepVII: Join LT and IT.

Thus LIFT is the required quadrilateral.

(ii) Construction:

StepI: Draw OL = 7.5 cm

Step II: Draw an arc with centre O and radius 10 cm.

StepIII: Draw another arc with centre L and radius 5 cm to meet the previous arc at D.

Step IV: Join OD and LD.

StepV: Draw an arc with centre L and D with equal radii of 6 cm to meet each other at G.

Step VI: Join LG and DG.

Thus GOLD is the required quadrilateral.

(iii) Construction: (The diagonals of a rhombus bisect each other at the right angle)

StepI: Draw BN = 5.6 cm.

Step II: Draw the right bisector of BN at O.

StepIII: Draw two arcs with centre O and radius 12 × DE, i.e., 12 × 6.5 = 3.25 cm to meet the right bisector at D and E.

Step IV: Join BE, EN, ND and BD.

Thus, BEND is the required rhombus.

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