Question

Find the length of each side of rhombus whose diagonals are of lengths 6cm and 8cm

Answer 1

Length of diagonals = 6cm and 8cm

Half the diagonals, 3cm and 4cm

The diagonals divide the rhombus in four right angled triangles.
(Since, the diagonals of rhombus intersect at right angles)

So, using Pythagoras theorem,

a²+b² = c²
3²+4² = c²
25 = c²
c = √25
c = 5 cm

So, one side of the rhombus is 5cm.

Answer 2

Let ABCD be rhombus
Let AC = 6 and BD = 8
property Diagonals of rhombus bisect each other in right angle.
consider AC and BD meet at O
THen in triangle AOD
AD² = AO² + OD²
= (AC/2)² + (BD/2)²
= 3² + 4²
= 25
AD = √25
AD = 5 side of rhombus