Question

The length of a rectangle of perimeter 64cm is of its breadth. Find the area of the
rectangle.

Answer 1

✰Correct Question :

• The length of a rectangle of perimeter 64 cm is 5/3rd of its breadth. Find the area of the rectangle?

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✰AnSwer :

• Let us consider breadth be b cm and length be 5b/3 cm.

$\implies$Perimeter of rectangle = 64 cm (Given)

$\implies$ 2 ( l + b ) = 64

$\implies$ l + b = 32

$\implies$ 5b/3 + b = 32

$\implies$ (5b + 3b)/3 = 32

$\implies$ 8b = 96

$\implies$ b = 96/8

$\implies$ b = 12 cm

Now, let us find length,

$\implies$ l = 5b/3

$\implies$ l = ( 5 × 12 )/3

$\implies$ l = 20 cm

Now, ATQ,

$\implies$Area of the rectangle = l × b

$\implies$Area of the rectangle = 20 × 12

$\implies$Area of the rectangle = 240 cm²

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Answer 2

$\sf{\underline{\boxed{\green{\large{\bold{ Question}}}}}}$

The length of a rectangle of perimeter 64 cm is 5/3rd of its breadth. Find the area of the rectangle?

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$\sf{\underline{\boxed{\green{\large{\bold{ Solution}}}}}}$

Let breadth be b cm and length be 5b/3 cm.

$\sf{\underline{\boxed{\blue{\large{\bold{ perimeter = 2 ( l + b )}}}}}}$

⟹ Perimeter of rectangle = 64 cm

⟹ 2 ( l + b ) = 64

⟹ l + b = 32

⟹ 5b/3 + b = 32

⟹ (5b + 3b)/3 = 32

⟹ 8b = 96

⟹ b = 96/8

⟹ b = 12 cm

$\sf{\underline{\boxed{\pink{\large{\mathfrak{\dag b = 12cm}}}}}}$

Now,

⟹ l = 5b/3

⟹ l = ( 5 × 12 )/3

⟹ l = 20 cm

$\sf{\underline{\boxed{\pink{\large{\mathfrak{\dag l = 20cm }}}}}}$

Now,

$\sf{\underline{\boxed{\green{\large{\bold{ area = l \times b}}}}}}$

⟹ Area of the rectangle = 20 × 12

⟹ Area of the rectangle = 240 cm²

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