Question

The diagonals of a rhombus are 16 cm and 12 cm . find the length of each side of

rhombus​

Answer 1

Answer:

10cm

Given,

Length of the diagonals of the Rhombus = 16cm , 12cm.

To Find :-

Length of each side of Rhombus.

Solution :-

Given that [According to Picture]

AC = 16cm

BD = 12cm

We know that :-

AC = AO + OC

BD = BO + OD

and :-

AO = OC

BO = OD

these are according to properties of Rhombus .

1) AC = AO + AO

AC = 2AO

16cm = 2 AO

AO = $\sf\dfrac{16cm}{2}$

AO = 8 cm.

2) BD = BO + BO

BD = 2BO

12cm = 2BO

BO = $\sf\dfrac{12cm}{2}$

BO = 6cm

We can observe that $\sf\angle AOB\: forms\: a \:Right \:Angle \:Triangle$

then :-

$\sf (AB)^{2} = (AO)^{2} + (OB)^{2}$

$\sf (AB)^{2} = (8cm)^{2} + (6)^{2}$

$\sf (AB)^{2} = 64cm^{2} + 36cm^{2}$

$\sf (AB)^{2} = 100cm^{2}$

Squaring on both sides :-

$\sf\sqrt{(AB)^{2}} = \sqrt{(10cm)^{2}}$

AB = 10cm

$\sf\therefore Length\: of\: all \:sides\: in\: a\: Rhombus\: are \:equal = AB = 10cm$

Answer 2

✔️Answer

In ΔAOD

(AD)

2

=(AO)

2

+(OD)

2

=36+64

AD

2

=100

AD=

100

=10cm

Rhombus has all sides equal

AB = AD = BC = CD = 10 cm