Question

Solve the following.

1) If the diagonals of a rhombus are of measure 10cm and 24cm. Find the sides of rhombus.​

Answer 1

hope it's helpful to you

Answer 2

Answer:

Given,

Diagonals of a Rhombus :-

• 10cm
• 24cm

To Find :-

Measure of Each side.

Solution :-

According to drawn picture :-

AC = 24cm

BD = 10cm

we know that,

1) AC = AO + OC

2) BD = BO + OD

3) AO = OC

4) BO = OD

5) All sides are equal in a Rhombus.

These are according to properties of Rhombus.

Then,

AC = AO + AO

AC = 2AO

24cm = 2AO

AO = $\sf\dfrac{24cm}{2}$

AO = 12cm

BD = BO + BO

BD = 2BO

10cm = 2BO

BO = $\sf\dfrac{10cm}{2}$

BO = 5cm

We can observe that $\sf\angle AOB \: forms \: a\:right\:angle\:Traingle$

i.e

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

$\sf (AB)^{2} = (12cm)^{2} + (5cm)^{2}$

$\sf (AB)^{2} = 144cm^{2} + 25cm^{2}$

$\sf (AB)^{2} = 169cm^{2}$

$\sf (AB)^{2} = (13cm)^{2}$

On squaring on both sides we get :-

AB = 13cm

$\sf\therefore Length\:of\:all\:sides\:in\:a\: Rhombus\:are\:equal = AB = 13cm$