Question

A wire bent in the shape of a rectangle of side 13.5 cm by 6.5 cm was straightened and rebent into a square. Find the length of the side of the square. ​

Answer 1

Answer: 10 cm

Step-by-step explanation:

To find the length of the wire , we need to find the perimeter of the rectangle

= 2(length+ breadth)

= 2( 13.5 cm + 6.5 cm)

=2× 20 cm

= 40 cm

Therefore, the length of the wire is 40 cm

To find the lenth of each side of the square we need to divide the lenth of the wire by 4

Therefore, 40 cm÷4

=10 cm

HOPE IT HELPS YOU☺️

Answer 2

Given :-

Length of the rectangle = 13.5 cm

Breadth of the rectangle = 6.5 cm

The same rectangle was re-bent into a square.

To Find :-

The length of the side of the square. ​

Analysis :-

First find the perimeter of the rectangle by substituting the given values in the formula of perimeter of rectangle.

Since the same rectangle was re-bent into a square, consider the perimeter too as of the rectangle.

Consider the side as a variable and substitute the values and get the vale of the side accordingly.

Solution :-

We know that,

• l = Length
• b = Breadth
• a = Area

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length+Breadth)}}$

Given that,

Length (l) = 13.5 cm

Breadth (b) = 6.5 cm

Substituting their values,

Perimeter = 2(13.5 + 6.5)

= 2(20)

= 40 cm

Therefore, the perimeter of the rectangle is 40 cm.

Let us consider the side to be 'x'.

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ square = 4 \times Side}}$

Since the same rectangle was re-bent into a square, the perimeter would be same for both.

Substituting their values,

$\sf 4x=40$

$\sf x=\dfrac{40}{4}$

$\sf x=10$

Therefore, each side of a square is 10 cm.