Question

The lengths of the diagonals of a rhombus
are 24 cm and 10 cm, respectively. Find
the length of all its sides.
please give step by step solution...and if possible please attach your solution work
​

Answer 1

Answer

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

Answer 2

Answer :

Length of all sides of rhombus are = 52cm.

Given :

• Length of sides of rhombus are 24 cm and 10 cm respectively.

To find :

• Length of all sides of rhombus.

★ $\large\underline\mathrm\red{Solution :-}$

Length of 1st diagonal [AC] = 24 cm.

Length of 2nd diagonal [BD] = 10 cm.

According to the condition to 2nd property,

Taking half of lenghts of diagonals

AO = 12 cm

BO = 5 cm

Now, Using Pythagoras theorem (PGT) for finding

side AB if a rhombus ,

→ AB² = AO² + BO²

→ AB² = (12)² + (5)²

→ AB² = 144 + 25

→ AB² = 169

→ AB = $\sqrt {169}$

$\boxed{→ \: AB \: = \: 13 \: cm}$

Now, AB = BC = CD = DA .......{ All sides of rhombus are equal} .

Length of all sides of rhombus = 13 + 13 + 13 + 13

→ 52 cm.

•°• Length of all sides of rhombus = 52 cm.