Question

the wire is in the shape of rectangle its length is 40 cm and width is 22 cm is the same wire is bent in the shape of square what will be the measure of each side also find which shape encloses more area

Answer 1

Perimeter of rectangle = length of wire
2(l+b) = 124cm.. Total length of wire = 124cm.
In square,
Perimeter of square = length of wire
4×side= 124
Side =124÷4=31cm
Area of rectangle = l×b= 40×22=880cm sq
Are of square = 31×31= 961sq cm
Square encloses more area

Answer 2

⭐ 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?

${\underline{\bf { Given \: that } }}$

• A wire is in the shape of a rectangle has length of 40 cm and breadth of 22 cm.

${\underline{\bf { To \: find: } }}$

• 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 and by how much?

${\underline {\bf { Solution : } }}$

According to question-

$\rm\blue {Perimeter \: of \: rectangle = Perimeter \: of \: square </p><p>}$

$\rm { \therefore 2(Length + Breadth) = 4 \times Side </p><p>}$

$\rm { \longrightarrow 2 (40 + 22) = 4 \times Side </p><p>}$

$\rm { \longrightarrow 2 \times 62 = 4 \times Side </p><p>}$

$\rm { \longrightarrow 124 = 4 \times Side </p><p>}$

$\rm { \longrightarrow Side = \dfrac{124}{4}</p><p>}$

$\rm\red { Side = 31 cm}$

Now,

$\rm {\implies Ar. \: of \:rectangle = length \times breadth }$

$\rm {\implies Ar. \: of \:rectangle = 40 \times 22 = 880 {cm}^{2} }$

and,

$\rm { \implies Area \: of \: square = {(Side)}^{2} }$

$\rm { \implies 31 \times 31 = 961 {cm}^{2} </p><p>}$

$\rm\purple { 880 {cm}^{2} < 961 {cm}^{2} }$

Therefore, the square-shaped wire encloses more area.