Question

A square is made with 10cm wire. if a rectangle is made with this wire and its length is 12cm.then find breadth of the rectangle ?whose area will be large, square or rectangular???​

Answer 1

Correct Question :

A wire is in the shape of a square of side 10cm . If the wire is rebent into a rectangle of length 12cm ,find its breadth & which figure encloses more area.

AnswEr :

$\textsf{Concept : when wire is used to make any} \\ \textsf{shape, and then it will turn into some other} \\ \textsf{shape. PERIMETER will be Same.}$

$\rule{75}{1}$

• Side of Square = 10 cm
• Length of Rectangle = 12 cm

$\underline{\bigstar\:\textsf{Let's Head to the Question Now :}}$

$\longrightarrow\texttt{Perimeter of Square = Perimeter of Rectangle}\\\\\\\longrightarrow\tt 4(Side) = 2(Length +Breadth)\\\\\\\longrightarrow\tt 4(10 cm) = 2(12 cm + Breadth)\\\\\\\longrightarrow\tt 40 cm = 2(12cm + Breadth)\\\\\\\longrightarrow\tt \dfrac{40 cm}{2}= 12cm + Breadth\\\\\\\longrightarrow\tt 20cm = 12cm + Breadth\\\\\\\longrightarrow\tt 20cm - 12cm = Breadth\\\\\\\longrightarrow \blue{\tt Breadth = 8cm}$

$\rule{170}{2}$

$\underline{\bigstar\:\textsf{Area of Both Shapes :}}$

$:\implies\texttt{Area of Square\qquad Area of Rectangle}\\\\\\:\implies\tt (Side)^2\qquad (Length \times Breadth)\\\\\\:\implies\tt(10 cm)^2\qquad(12cm \times 8cm)\\\\\\:\implies \boxed{ \green{\tt 100 cm^2 \quad > \quad96cm^2}}$

⠀

∴ Area of Square will be Larger.

Answer 2

Answer:

${\boxed{\bold\green{Breadth =8\:cm }}}$

${\boxed{\bold\purple{Area\:of\:square\:is \:large}}}$

Step-by-step explanation:

When the rectangle is made with this wire then perimeter of square = perimeter of rectangle.

Given:-

• Side of square = 10 cm
• Length of rectangle = 12 cm

$\rule{300}{1}$

$\implies\sf Perimeter\:of\:square = Perimeter \:of\:rectangle \\\\\implies\sf 4 \times Side = 2(length + breadth) \\\\\implies\sf 4 \times 10 = 2(12+breadth) \\\\\implies\sf 40 = 24 + 2Breadth \\\\\implies\sf 2Breadth = 40 - 24 \\\\\implies\sf Breadth =\cancel{\dfrac{16}{2}} \\\\\implies{\boxed{\sf{ Breadth = 8\:cm}}}$

$\rule{300}{1}$

${\boxed{\sf\green{Area \:of\:square = {(Side)}^{2}}}} \\\\\implies\sf Area\:of\:square ={(10)}^{2} \\\\\implies{\boxed{\sf{Area\:of\:square =100\:{cm}^{2} }}}$

$\rule{300}{1}$

${\boxed{\sf\green{Area\:of\:rectangle = Length \times Breadth }}}\\\\\implies\sf Area\:of\:rectangle = (12\times 8)\:{cm}^{2} \\\\\implies{\boxed{\sf{Area\:of\:rectangle = 96\:{cm}^{2} }}}$

$\because\bold{100\:{cm}^{2} > \:96\:{cm}^{2} }$

$\therefore\bold{Area\:of\:square\:is\:bigger.}$