Question

A wire is in the shape of a rectangle .its length is 40cm and breadyh 22 cm.if the same wire is rebent in the shape of a square ,what will measure of each side, also find which shape encloses more area?

Answer 1

perimeter of rectangle =2*l+b

2*40+22 =124cm

perimeter of rectangle=perimeter of square

perimeter of square= 4*s
124 = 4*s
124/4=s
side=31

area of rectangle=l*b
40*22=880sqcm
area of square=s*s
31*31= 961sqcm
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.