Question

A wire is in the shape of a square if side 10cm .if the wire is rebent into a rectangle of length 12cm ,find its breadth which figure encloses more area and by how much

Answer 1

You may prefer this pic.
Hope it helps.
The square encloses more area by 4 cm sq.

Answer 2

Answer:

The square encloses more area by $4 cm^2$.

To find:

Which figure encloses more area and by how much more they enclosed the area compared to the another figure.

Solution:

Given, Side of the square: 10 cm  

Hence, Perimeter of the square = 4 X 10 = 40 cm = Length of the wire.

When wire is re-bend to make a rectangle,

Given, Length of the rectangle= 12 cm  

Let the breadth of the rectangle be b  

Thus, the perimeter of both the rectangle and the square is same  since the square is stretched to make a rectangle.

We know that the Perimeter of rectangle  

$\begin{array} { c } { = 2 ( l + b ) = 2 ( 12 + b ) } \\\\ { 40 = 24 + 2 b } \\\\ { 2 b = 40 - 24 \Rightarrow 2 b = 16 } \\\\ { b = 8 \mathrm { cm } } \end{array}$

Area of enclosed by the square

$= ( \text {side} ) ^ { 2 } = 10 \times 10 = 100 \mathrm { cm } ^ { 2 }$

Area enclosed by the rectangle

$= ( \text {length} ) \times ( \text {breadth} ) = 12 \times 8 = 96 \mathrm { cm } ^ { 2 }$

Thus, Difference in their area

$= ( 100 - 96 ) c m ^ { 2 } = 4 c m ^ { 2 }$

Hence, the square encloses more area by $4 cm^2$.