# Construct the following and give justification :A rhombus whose diagonals are 4 cm and 6 cm in lengths.

Given : Rhombus with diagonals length = 4 cm, 6 cm

Steps of Construction :

1.         Draw a line AB = 4 cm

2.         Bisect the AB using another line EF which intersects it at point X

E X F is perpendicular to AB

3.         As center X mark an arc of 3 cm as the radius on XF and XE which intersects at C and D respectively.

4.         Join AD, AE, BC, BD

ACBD is the required rhombus.

Justification :

$DC\perp AB$ hence  DA = DB, AC = BC   …..(1)

{every point on perpendicular bisector of line is equidistance from end points of line}

$\angle DXB=90^{\circ}$

Also,    XD = XC = 3 cm

Thus,   AB is perpendicular to DC

BD = BC         …..(2)

From 1 and 2, ABCD is a rhombus.

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