Question

Find the length of the side of a rhombus whose diagonals are of lengths 12 cm and 16 cm.
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Answer 1

Answer:

10cm.

Explanation:

In rhombus ABCD,

BD=16cm (Given)

•°•BO=DO=8cm (Diagonals of a rhombus bisect each other)

AC=12cm (Given)

•°•AO=CO=6cm (Diagonals of a rhombus bisect each other)

Now, in triangle BOC,

BO=8cm (Proven above)

CO=6cm (Proven above)

Angle BOC=90° (Diagonals of a rhombus bisect each other at 90°)

•°•(BC)^2=(BO)^2+(CO)^2

•°•(BC)^2= (8)^2 + (6)^2

•°•(BC)^2= 64+36

•°•(BC)^2=100

•°•BC=under root 100

•°•BC=10cm

•°•AB=BC=CD=DA=10cm (All sides of a rhombus are equal).