Question

The diagonal of the rhombus are 48cm and 20cm long. Find area and perimeter of the rhombus.​ ​

Answer 1

$\huge\underline{\boxed{\mathfrak{\red{Given}}}}$

• The diagonal of the rhombus = 48cm & 20cm long.

$\huge\underline{\boxed{\mathfrak{\green{To \ find}}}}$

• Area and perimeter of the rhombus

$\huge\underline{\boxed{\mathfrak{\blue{Solution}}}}$

Area of rhombus = ½ × product of diagonals

→ ½ × AC × BD

→ ½ × 48 × 20

→ 24 × 20

→ 480 cm²

$\texttt{AO = OC = 48/2 = 24 cm }$

$\texttt{BO = OD = 20/2 = 10 cm }$

Now in ∆ AOB, By Pythagoras theorem

➪ (AB)² = (BO)² + (AO)²

➪ AB² = (10)² + (24)²

➪ AB² = 100 + 576

➪ AB = √676

➪ AB = 26 cm

$\bf AB \:=\: BC\: =\: CD\: = \:DA\: =\: 26 cm$

Now, Perimeter of rhombus = 4 × a

➵ 4 × 26

➵ 104 cm

Hence,

$\:\:\:\bullet\:\:\bf Area \:of\: Rhombus \: =\: {\orange{480 \:cm^2}}$

$\:\:\:\bullet\:\:\bf Perimeter\: of \:Rhombus\: =\: {\orange{104 \:cm}}$

Answer 2

Answer:

The diagonal of the rhombus = 48cm & 20cm long.

\huge\underline{\boxed{\mathfrak{\green{To \ find}}}}To find

Area and perimeter of the rhombus

\huge\underline{\boxed{\mathfrak{\blue{Solution}}}}Solution

Area of rhombus = ½ × product of diagonals

→ ½ × AC × BD

→ ½ × 48 × 20

→ 24 × 20

→ 480 cm²

\texttt{AO = OC = 48/2 = 24 cm }AO = OC = 48/2 = 24 cm 

\texttt{BO = OD = 20/2 = 10 cm }BO = OD = 20/2 = 10 cm 

Now in ∆ AOB, By Pythagoras theorem

➪ (AB)² = (BO)² + (AO)²

➪ AB² = (10)² + (24)²

➪ AB² = 100 + 576

➪ AB = √676

➪ AB = 26 cm

\bf AB \:=\: BC\: =\: CD\: = \:DA\: =\: 26 cmAB=BC=CD=DA=26cm

Now, Perimeter of rhombus = 4 × a

➵ 4 × 26

➵ 104 cm

Hence,

\:\:\:\bullet\:\:\bf Area \:of\: Rhombus \: =\: {\orange{480 \:cm^2}}∙AreaofRhombus=480cm2

\:\:\:\bullet\:\:\bf Perimeter\: of \:Rhombus\: =\: {\orange{104 \:cm}}∙PerimeterofRhombus=104cm