Question

a wire is in the shape of a square of side 14cm. if the same wire is rebent in the shape of a rectangle whose length and breadth are in the ratio 4:3, then what will be the dimension of the rectangle? also find which shape encloses more area.

Answer 1

Hello Friend !!!

Side of the square = 14cm
Perimeter of the square = Length of the wire = 14 x 4 = 56cm
⇒Perimeter of the rectangle is also = 56cm 
Let, the length and breadth of the rectangle be 4x and 3x.

⇒ 2 ( 4x + 3x ) = 56
⇒ 8x + 6x = 56
⇒ 14x = 56
⇒ x = 4 
So, length = 4 x 4 = 16cm and 
      breadth = 4 x 3 = 12cm 



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Answer 2

hiii!!!

here's ur answer...

ATQ,

the same wire is rebent into rectangle.

therefore perimeter of square = perimeter of rectangle

given the side of the square = 14cm

perimeter of the square = side × 4

= 14 × 4

= 56cm

therefore perimeter of the rectangle is also 56cm.

given the Length and breadth of the rectangle are in ratios. let the Length and breadth be 4x and 3x.

==> 2 ( l + b ) = 56cm

==> 2 ( 4x + 3x ) = 56cm

==> 8x + 6x = 56

==> 14x = 56

==> x = 56/14

==> x = 4

==> x = 4

hence, Length of the rectangle = 4x

= 4 × 4

= 16cm

breadth of the rectangle = 3x

= 3 × 4

= 12cm

VERIFICATION:-

perimeter of the rectangle = 2 ( l + b )

= 2 ( 16 + 12 )

= 2 × 28

= 56cm

hence verified

now,

area of the square = side²

= 14 × 14

= 196cm²

area of the rectangle = l × b

= 16 × 12

= 192cm²

area of square is more by = 196 - 192

= 4cm²

hope this helps..!!