Question

area of rohmbus is 120 cm ^2 and it's one diagonal is 24 . then find each side . please don't spam . ​

Answer 1

Hello, Buddy!!

Given:-

• Area of Rhombus is 120cm²
• Diagonal[d1] of Rhombus = 24cm

To Find:-

• Length of each side.

Required Solution:-

Let,

ABCD be the Rhombus

Other Diagonal be d2

• Area of Rhombus = 1/2×d1×d2 sq.units.

→ 1/2×AC×BD = Area of Rhombus

→ 1/2×24×d2 = 120

→ 12×d2 = 120

→ d2 = 120/12

→ d2 = 10cm

• Length of Other Diagonal = 10cm

Let,

O be the point where the two diagonals intersect each other.

Then, AO = OC = 24/2 → 12cm

BO = OD = 10/2 → 5cm

WKT, Diagonals of a Rhombus are Perpendicular to each other.

Take, ∆AOB

In which ∠AOB = 90°[AO⊥BD]

By Pythagoras Theorem

→ (AB)² = (AO)²+(OB)²

→ (AB)² = (12)²+(5)²

→ (AB)² = 144+25

→ AB = √(169)

→ AB = √(13)²

→ AB = 13

WKT, In a Rhombus all sides are equal

→ AB=BC=CD=DA

• Length of Side of Rhombus ☞ 13cm

@MrMonarque♡

Hope It Helps You ✌️

Answer 2

Area of a rhombus= 1/2×product of its diagonals

Area of a rhombus=

21 ×d1 ×d2

⇒120=2

1×20×d2

⇒d 2 = 20

120×2

=12cm

∴ the other diagonal is 12cm

Give me some multiple thanks

Mark Branlist please