Question

rectangle and Square have the same perimeter 100 cm. find the side of a square. if the rectangle has a breadth 2 cm less than that of the square. find the breadth, length and area of the rectangle.​

Answer 1

Solutions :-

Given :

Perimeter of rectangle = Perimeter of Square = 100 m

Find the side of the square :-

Perimeter of Square = 4 × side

=> 100 m = 4 × Side

=> Side = 100/4 = 25 m

Breadth of rectangle = (side of square - 2) m

= (25 - 2) m = 23 m

Let the length of rectangle be x

Find the length of rectangle :-

Perimeter of rectangle = 2(Length +Breadth)

=> 100 = 2(x + 23)

=> 100/2 = x + 23

=> 50 - 23 = x = 27 m

Find the area of rectangle :-

Area of rectangle = (Length × Breadth) sq. units

= (27 × 23) m²

= 621 m²

Hence,

Length of Rectangle = 27 m

Area of rectangle = 621 m²

Answer 2

Side of square = 25 cm.

Breadth of rectangle = 23 cm.

Length of rectangle = 27 cm.

Area of rectangle = 621 cm².

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Step by step explanation:-

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Given:-

• Rectangle and square are of same perimeter that is 100 cm.

To find:-

• Side of square.
• Length and Breadth of rectangle.
• Area of rectangle.

$\large\tt\blue{SolutioN:-}$

Perimeter of square = 4a

In which 'a' is side of square.

⇒ 100 = 4 × a

⇒100/4 = a

⇒a = 25 cm.

Side of square is 25 cm.

Given that,

Breadth of rectangle is a-2 ( a is side of square)

⇒25 - 2

⇒23

So, Breadth of rectangle is 23 cm.

Perimeter of rectangle = 2 (l + b)

⇒ 100 = 2 × (23 + l)

⇒100 = 46 + 2l

⇒100 - 46 = 2l

⇒54 = 2l

⇒54/2 = l

⇒l = 27 cm.

Length of rectangle is 27 cm.

Area of rectangle = l × b

⇒27 × 23 cm²

⇒621 cm²

Area of rectangle is 621 cm².