a wire in the shape of a rectangle it is length is 40 and breath is 22 if the same wire is rebent in the shape of a square what will be the measure of each side. Created by sofia53. Math

Here, area of rectangle= area of squarearea of rectangle = 40×22=880area of square = s^2=880 s=√880

a wire in the shape of a rectangle it is length is 40 and breath is 22 if the sa...

⭐ 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-

$\rm\blue {Perimeter \: of \: rectangle = Perimeter \: of \: square }$

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

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

$\rm { \longrightarrow 2 \times 62 = 4 \times Side }$

$\rm { \longrightarrow 124 = 4 \times Side }$

$\rm { \longrightarrow Side = \dfrac{124}{4}}$

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

Now,

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

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

and,

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

$\rm { \implies 31 \times 31 = 961 {cm}^{2} }$

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

Therefore, the square-shaped wire encloses more area.

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