Question

A rectangle and a square have the same perimeter 100 cm. Find the side of the 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

Answer :

• Length of rectangle is 27cm
• Breadth of rectangle is 23cm
• Area of rectangle is 621cm²

Given :

• A rectangle and a square have the same perimeter 100 cm.
• The rectangle has a breadth 2 cm less than that of the square.

To find :

• Side of the square
• breadth, length and area of the rectangle.

Solution :

Given,

• Perimeter of rectangle = Perimeter of square = 100cm

● We need to find the sides of the square :

We know that

• Perimeter of square = 4 × sides

⇥ Perimeter of square = 4 × sides

⇥ 100 = 4 × sides

⇥ sides = 100/4

⇥ Sides = 25cm

Side of a square is 25cm.

• Let the length of rectangle be x

Given,

If the rectangle has a breadth 2cm less than that of the square so,

● Finding the breadth of rectangle :

⇥ Breadth of rectangle = (side of square - 2) cm

⇥ breadth of rectangle = 25 - 2

⇥ Breadth of rectangle is 23cm

Breadth of rectangle is 23cm

● Finding the length of rectangle :

• let the Length of rectangle be x

We know that

• Perimeter of rectangle is 2(length + breadth)

⇥ Perimeter of rectangle = 2(l + b)

⇥ 100 = 2(x + 23)

⇥ x + 23 = 100/2

⇥ x + 23 = 50

⇥ x = 50 - 23

⇥ x = 27cm

Length of rectangle is 27cm.

● Finding the area of rectangle :

We know that

• Area of rectangle is length × breadth

⇥ Area of rectangle is length × breadth

⇥ Area of rectangle = 27 × 23

⇥ Area of rectangle = 621cm²

Area of rectangle is 621cm²

Hence,

• Length of rectangle is 27cm
• Breadth of rectangle is 23cm
• Area of rectangle is 621cm²