Question

A wire is in the shape of a square of side 10cm If the wire is rebent into a rectangle of length 12cm, find its breadth Which encloses more area , the square or the rectangle​

Answer 1

Given:

Side of the square: 10 cm

Length of the rectangle: 12 cm

To find:

• The breadth of the rectangle.
• Compare the area of the rectangle and square.

Solution:

Breadth of the rectangle:

In order to find the breadth of the rectangle we will first have to find the length of the wire.

We can find out the length of the wire by calculating the perimeter of the square:

Perimeter of the square = 4 × side

                                        = 4 × 10

                                        = 40 cm

∴ The length of the wire = 40 cm

Now, since the same wire is reshaped into the rectangle the perimeter remains the same.

∴ Perimeter of rectangle = 40 cm

2( L + B ) = 40

2( 12 + B ) = 40

∴Breadth = 8 cm

Comparing the area of the two shapes

Area of square = Side²

                         = 100 cm²

Area of rectangle = L × B

                              = 12 × 8

                              = 96 cm²

Now, comparing the areas of both the shapes the area of square is greater than rectangle.

∴The breadth of the rectangle is 8 cm and the square encloses more area compared to rectangle.