A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

Solution: Let us see what happens when a wire is in the shape of a rectangle and is rebent in the shape of a square. Here, we are discussing about the boundary of the square and rectangle. This means we need to know the perimeter of the rectangle and square. Since we are using the same wire to make the square, the perimeter of the rectangle will be the same as the perimeter of the square.

perimeter of square = perimeter of rectangle

Let us find the perimeter of the rectangle and use it to find the side of the square.

Length of the rectangle = 40 cm

Breadth of the rectangle = 22 cm

Using this equation we can find the length of the side of the square.

4 × Side = 2 (Length + Breadth)

4 × Side = 2 (40 + 22)

4 × Side = 2 × 62

4 × Side = 124

Side = 124/4

Side of square = 31 cm

Now, let us find the area of the square to check which shape encloses more area.

Area of square = side × side

= 31 cm × 31 cm

= 961 cm²

Area of rectangle = Length × Breadth

= 40 cm × 22 cm

= 880 cm²

Hence, we can see that the area of the square is 961 cm² and the area of the rectangle is 880 cm². This shows that the square shape encloses more area.

This shows that when a wire is in the shape of a rectangle and is rebent in the shape of a square, we can easily find the side of the square and compare the areas.

☛ Check: NCERT Solutions for Class 7 Maths Chapter 11

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Video Solution:

A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

Class 7 Maths NCERT Solutions Chapter 11 Exercise 11.1 Question 6

Summary:

A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, the measure of each side will be 31 cm. Also, square shape encloses more area.

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