Question

4. A wire is in the shape of a rectangle. Its length is 32.1 cm and breadth is 21.9 cm. If the same wire is rebent
in the shape of a square, what will be the measure of each side. Also find which encloses more area?​

Answer 1

Answer:

• Each side of the square is 27cm
• The area of the square is larger

Explanation:

The wire was in the shape of a rectangle, the measurements of the wire:

• Length of the rectangle = 32.1cm
• Breadth of the rectangle = 21.9cm

Perimeter of a rectangle: 2( length + breath )

Perimeter = 2( 32.1cm + 21.9cm )

Perimeter = 2( 54cm )

Perimeter = 108cm

Area of a rectangle = Length × Breath

Area = 32.1cm × 21.9cm

Area ≈ 703cm²

As the same wire was rebent into a square, The perimeter of the square must be equal to the perimeter of the rectangle.

Perimeter of the rectangle = Perimeter of the square

Perimeter of the square = 108cm

Perimeter of a square = 4 × side

⟹ 108cm = 4 × side

⟹ 108cm/4 = side

⟹ 27cm = side

The the measure of each side of the square is 27cm

Area of a square = (Side)²

Area of the square = (27cm)²

Area of the square = 729cm²

729cm² > 703cm²

So, the area of the square is larger than the rectangle's area.

Answer 2

Answer:

• Measure of each side of square = 27cm.

• Square encloses more area than rectangle.

Step-by-step explanation:

Let the side of the square be x.

Since same amount of wire is used in both rectangle and square, therefore their perimeter will be equal.

Perimeter of rectangle = Perimeter of square

→ 2(Length + Breadth) = 4 × x

→ 2(32.1cm + 21.9cm) = 4x

$\rm\dashrightarrow 32.1cm + 21.9cm = \dfrac{ 4x}{2}$

$\rm\dashrightarrow 32.1 cm+ 21.9 cm = 2x$

$\rm\dashrightarrow 2x = 54 cm$

$\rm\dashrightarrow x = \dfrac{54cm}{2}$

$\rm\dashrightarrow\bf x = 27 cm$

$\therefore \qquad \rm Measure\ of\ each\ side \ of \ the \ square \ will \ be \ 27cm$

Now we have to compare the area of rectangle and square.

Area of Rectangle

= Length × Breadth = 32.1cm × 21.9cm = 702.99 cm² or 703 cm² (approx.).

Area of square

= side × side = 27cm × 27cm = 729 cm²

Clearly,

729 cm² > 703 cm²

Hence,

Area of square > Area of rectangle.