Question

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?​

Answer 1

Answer:

Answer :- Measure of each side of square is :- 31 cm. Area of square is more

Answer 2

A n s w e r

G i v e n

• Wire is in the shape of a rectangle

• Length of rectangle is 40 cm

• Breadth of rectangle is 22 cm

F i n d

• Side of square if the same wire is rebent in the shape of a square

• Shape which encloses more area

S o l u t i o n

As the wire which is in the shape of rectangle is rebend to square hence the perimeter of wire will be same in both cases

$\underline{ \underline{\bold{\texttt{Perimeter of rectangular wire :}}}}$

➠ 2(Length + Breadth)

• Length = 40 cm

• Breadth = 22 cm

⟮ Putting the above values ⟯

: ➜ 2(Length + Breadth)

: ➜ 2(40 + 22)

: ➜ 2(62)

: : ➨ 124 cm ⚊⚊⚊⚊ ⓵

• Hence the perimeter of wire in shape of rectangle is 124 cm

$\underline{ \underline{\bold{\texttt{Perimeter of square wire :}}}}$

➠ 4(Side) ⚊⚊⚊⚊ ⓶

Equation ⓵ = Equation ⓶

[ As the perimeter will remain same ]

Thus ,

: ➜ 124 = 4(Side)

: ➜ $\sf Side = \dfrac { 124 } { 4 }$

: : ➨ Side = 31 cm

• Hence the side of square formed by wire is 31 cm

$\underline{ \underline{\bold{\texttt{Area of rectangular wire :}}}}$

➠ Length × Breadth

• Length = 40 cm

• Breadth = 22 cm

⟮ Putting the above values ⟯

: ➜ Length × Breadth

: ➜ 40 × 22

: : ➨ 880 sq. cm ⚊⚊⚊⚊ ⓷

• Hence wire in shape of rectangle covers 880 sq. cm of area

$\underline{ \underline{\bold{\texttt{Area of square wire :}}}}$

➠ (Side)²

• Side = 31 cm

⟮ Putting the above value ⟯

: ➜ (Side)²

: ➜ (31)²

: : ➨ 961 sq. cm ⚊⚊⚊⚊ ⓸

• Hence wire in shape of square covers 961 sq. cm of area

From equation ⓷ & ⓸

• Hence we got that the wire in shape of square encloses more area than rectangle