Question

The length of diagonals of a rhombus are 24cm and 10cm. The length of each side
of a rhombus is

Answer 1

THEREFORE, LENGTH OF EACH SIDE OF A RHOMBUS IS 13cm .

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Answer 2

$\underline{ \underline{ \Large \pmb{\mathit{ {Given:}} }} }$

• The length of diagonals of a rhombus are 24cm and 10cm.

$\underline{ \underline{ \Large \pmb{\mathit{ {To \: calculate:}} }} }$

• The length of each side of a rhombus.

$\underline{ \underline{ \Large \pmb{\mathit{ {Calculation:}} }} }$

✰ Here, we are given that the length of diagonals of a rhombus are 24cm and 10cm. We have to find the length of each side of a rhombus .In order to calculate the length of each side of a rhombus, we'll use the properties of the rhombus. And by using the pythagoras property we'll find the length of each side of a rhombus.

⠀⠀⠀⠀⠀_____________

Let's make the diagram first. So, it'll be easy to understand the concept & the question. [Refer to the attachment.]

Say the rhombus as ABCD. As we know that,

• Diagonals of a rhombus bisect each other. [ Here, O is the point where the diagonals are bisecting each other. ]

So,

→ AO = OC

→ AC = AO + OC

→ 10 cm = AO + OC

Let's say AO and OC as y each. ( Since, they are equal.)

→ 10 cm = y + y

→ 10 cm = 2y

→ $\sf {\dfrac{10}{2} }$ cm = y

→ 5 cm = y

Therefore,

→ AO = 5 cm

→ OC = 5 cm

Similarly,

→ DO = OB

→ DB = DO + OB

→ 24 cm = DO + OB

Let's say DO and OB as z each. ( Since, they are equal.)

→ 24 cm = z + z

→ 24 cm = 2z

→ $\sf {\dfrac{24}{2} }$ cm = ,

→ 12 cm = z

Therefore,

→ DO = 12 cm

→ OB = 12 cm

Now, as we know that :

• Diagonals of a rhombus bisect each other at 90° & all the sides of a rhombus are equal.

So, here we can find the length of its side by pythagoras property. Rhombus is divided into 4 right angles of same base, hypotenuse and perpendicular.

As all the sides of a rhombus are equal, so let's find only the one side of the rhombus now. All the sides will be of the same length.

Let,

In ∆ ABO :

• AB = Side (hypotenuse) or x

• AO = Height

• OB = Perpendicular

By using pythagoras property,

→ H² = B² + P²

→ AB² = AO² + OB²

→ x² = 5² + 12²

→ x² = 25 + 144

→ x² = 169 cm

→ x =√169

→ x = 13

So,

→ AB = 13 cm

Therefore,

$\dag \: \: \sf \purple {Side \: of \: rhombus \: is \: 13 \: cm. }$