Question

3. The lengths of the diagonals of a rhombus
are 24 cm and 10 cm, respectively. Find
the length of all its sides.



If you will give correct and full solution so I will mark your solution as brain list​

Answer 1

Step-by-step explanation:

Let ABCD be the rhombus where, AC=10cm and BD=24cm

Let AC and BD intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.

Thus, we have

AO=

2

1

×AC=

2

1

×10=5cm and

BO=

2

1

×BD=

2

1

×24=12cm

In right angled △AOB,

⇒ (AB)

2

=(AO)

2

+(BO)

2

⇒ (AB)

2

=(5)

2

+(12)

2

⇒ (AB)

2

=25+144

⇒ (AB)

2

=169

∴ AB=13cm

∴ The length of each side of rhombus is 13cm.

solution

Answer 2

Length of all sides of rhombus = 52 cm

Given

The lengths of the diagonals of a rhombus are 24 cm and 10 cm, respectively

To Find

Length of all its sides or simply Perimeter

How to Solve

Revise two properties of rhombus

1 . All sides of rhombus are equal

2 . Diagonals of rhombus bisect each other

___________________________

We have lengths of two diagonals . So , we can know the length of side of rhombus easily by applying Pythagoras theorem .

Solution

Find attachment for diagram

Given

AC = 24 cm

[ ∵ Length of 1st diagonal ]

BD = 10 cm

[ ∵ Length of 2nd diagonal ]

Now , A/c to 2nd property ,

AO = 12 cm [ ∵ half of 24 cm ]

BO = 5 cm [ ∵ half of 10 cm ]

Apply Pythagoras theorem for finding AB , Length of side of rhombus ,

⇒ AB² = AO² + BO²

⇒ AB² = (12)² + (5)²

⇒ AB² = 144 + 25

⇒ AB² = 169

⇒ AB = 13 cm

Now , AB = BC = CD = DA

[ ∵ A/c to 2nd property All sides of a rhombus are equal . ]

So ,

Perimeter of rhombus = AB + BC + CD + DA

⇒ 13 + 13 + 13 + 13

⇒ 52 cm

So , length of all sides of rhombus = perimeter = 52 cm

❤️Hope it helps you, ❤️