Question

using a Pythagoras theorem find the length of second diagonal of a rhombus of side 5 cm and having one of its diagonal as 8 cm​

Answer 1

Step-by-step explanation:

ABCD is a rhombus, where AC and BD are the diagonals.

Side of the rhombus is 5cm

BD=8cm

We know that, diagonals of rhombus perpendicularly bisect each other.

∴ BO=4cm

In right angled △AOB,

⇒ (AB)

2

=(AO)

2

+(BO)

2

[ By Pythagoras theorem ]

⇒ (5)

2

=(AO)

2

+(4)

2

⇒ 25=(AO)

2

+16

⇒ (AO)

2

=9

∴ AO=3cm

⇒ AC=2×3=6cm

∴ The length of other diagonal is 6cm.