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?

Given

From the given details we get to know that

Length of the rectangle = 40 cm

Breadth of the square = 22 cm

The perimeter of the square is the same as the perimeter of a rectangle

Find out

We have to determine the measure of each side and which shape encloses the maximum area

Solution

From the given data

The perimeter of the rectangle = Perimeter of the Square

The perimeter of the rectangle is given by = 2(Length + Breadth)

The perimeter of the square is given by= 4 x side of the square

 2 (Length + Breadth) = 4 × side

2 (40 + 22) = 4 × side

2 (62) = 4 × side

124 = 4 × side

Side = 124/4

Side = 31 cm

 The area of the rectangle is given by = (Length × Breadth)

= 40 × 22

= 880 cm2

Area of square = side2

= 312

= 31 × 31

= 961 cm2

∴Square shaped wire encloses more area.

Answer

The measure of each side of the square is 31cm

Square shaped wire encloses more area.

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