Question

The diagonals of a rhombus ABCD intersects at O.If AC=16cm and BD=12cm.Find the length of the sides ?

Answer 1

Answer :- Length of the sides = 10cm

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Given :-

• ABCD is a rhombus

• Diagonals intersect at O.
• AC = 16cm

• BD = 12cm

To Find :-

Length of the sides

Solution :-

In rhombus ABCD,

we know that in a rhombus diagonals intersect each other perpendicularly.

Therefore,

AO = 8cm

OC = 8cm

BO = 6cm

OD = 6cm

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They bisect perpendicularly hence,

∠BOC = 90°

By Pythagoras theorem :-

CO² + BO² = CB²

8² + 6² = CB²

64 + 36 = CB²

CB = √100

CB = 10cm

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Length of 1 side = 10cm

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All sides of  a rhombus are equal, Therefore

Length of the sides = 10cm

Answer 2

$\mathfrak{\large{\underline{\underline{Answer:-}}}}$

Length of the sides = 10cm

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

To Find :

Length of the rhombus's sides.

Given that :

ABCD is a rhombus. So, Diagonals intersect at O.

AC = 16cm

BD = 12cm

Solution :

In ∆AOB

We know that,

Pythagoras theorem :

Square of the length of the hypotenuse is same to the sum of squares of lengths of other two sides of the right-angled triangle.

So,

$\sf \longrightarrow H^2=P^2+B^2\\\sf \longrightarrow H^2=8^2+6^2\\\sf \longrightarrow H^2=64+36\\\sf \longrightarrow H=\sqrt100\\\sf \longrightarrow H=10cm$

We also know that,

The all sides are same of rhombus.

So,

All sides are equal (10 cm.)