Question

6. 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?
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Answer 1

Answer:

Measure of each side of square wire is 31 cm

The square wire encloses more area.

Explanation:

Perimeter of the rectangular wire=2(length+breadth)

=2(40+22)

=2*62

=124 cm

Since the same wire is rebent in the shape of a square, therefore its boundary,that is, perimeter remains the same

perimeter of the square wire=124 cm

measure of each side=perimeter/4

=124/4 cm

= 31cm

Area of rectangular wire=length*breadth

= 40*22 cm2

= 880 cm2

area of square wire= s*s

= 31*31 cm2

=961 cm2

Therefore the square wire encloses more area.

Answer 2

Given:

Length of the rectangle = 40 cm

Breadth of the square = 22 cm

Then we will get:

Perimeter of the rectangle = Perimeter 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

So, Area of the rectangle = (Length × Breadth)

= 40 × 22

= 880 cm²

Area of square = side²

= 312

= 31 × 31

= 961 cm²

∴Square shaped wire encloses more area.