Question

a wire in the shape of a square of side 20 cm. if the wire is rebent into a rectangle of length 22 cm,find breadth. which encloses more area square or rectangle

Answer 1

$let \: \: breadth \: \: be \: \: x \\ perimeter \: \: of \: \: both \: \: should \: \: be \: same \\ 2(22 + x) = 4 \times 20 \\ x = 40 - 22 = 18 \: cm \\ \\ area \: of \: square = {20}^{2} = 400 \\ area \: of \: rectangle = 22 \times 18 = 396 \\ so \: \: area \: of \: square \: is \: more$

Answer 2

Perimeter of square = 4 × side

= 4 × 20

= 80cm

Now P of square = P of rectangle

80 = 2(L + B)

80 = 44 + 2B

B = 36 / 2 = 18cm

Area of aquare = side × side

= 20 × 20

= 400cm^2

Area of rectangle = L × B

= 22 × 18

= 396cm^2

Hence Area of aquare is more.

Thanks