Question

A wire is in the shape of a square of side 20 cm. If the wire is rebent into a rectangle of length 22 cm, find its breadth. Which encloses more area the square or the rectangle?​

Answer 1

${ \large{ \underline{ \pmb{ \frak{Given \: that : }}}}}$

★ A wire is in the shape of a square of side 20 cm

★ the wire is rebent into a rectangle of length 22 cm,

${ \large{ \underline{ \pmb{ \frak{ To \: Find : }}}}}$

★ The breadth of the rectangle

★ The area of the square with side 20cm

★ The area of the rectangle by finding its dimensions

★ Compare the area of the rectangle and the area of the square and state which is greater

${ \large{ \underline{ \pmb{ \frak{Understanding \: the \: concept : }}}}}$

☀️ Concept : Here, we have been provided with the side Of the square which is 20cm And said that the wire which was used to form the square was again rebent to form a rectangle with length 22cm .

❍ Which,makes it clear that the perimeter of both the rectangle and the square is the same as the same length of wire Is used to form the rectangle So, Now let's find the Perimeter of the square which will help us in finding the breadth of the rectangle and so, that we can find the area's of the following figures and then compare them

${ \large{ \underline{ \pmb{ \frak{Let's \: use \: the \: concept : }}}}}$

★ Formula to find the perimeter of a square ( according to the given measurements) = 4 times the side of the square

which will help us in getting to know about the perimeter of the rectangle as they measure the same

★Formula to find the breadth of the rectangle (according to the given measurements) = 2( length + breadth) here, let's substitute the value of the perimeter which we found with the help of the side of a square and the length which is given in the question above

★ Formula to find the area of the square ( According to the question) = side time side or side².

★ Formula to find the area of the rectangle (According to the question) = length times the breadth of the rectangle

${ \large{ \underline{ \pmb{ \frak{ Solution : }}}}}$

★ Breadth of the rectangle is 18cm

★ Area of the rectangle is 396cm² and the area of the square is 400cm² Thus the square encloses more area compared to the rectangle

${ \large{ \underline{ \pmb{ \frak{ Full \: solution: }}}}}$

~ Firstly let's find the perimeter of the square which would futher further help us to find the breadth of the rectangle.

Let's start now.!

~ Using the above mentioned concept

✪ Perimeter of a square = 4 × side

➠ Perimeter of the square = 4 × side

➠ Perimeter of the square = 4 × 20cm

➠ Perimeter of the square = 80cm

• Therefore, Perimeter of the square = 80cm

~Now as we know that the perimeter of the rectangle is also the same as the same wire is rebent to form it . So, perimeter of the rectangle = 80cm

~ Now, let's find the breadth of the rectangle using the above mentioned concept substituting the values of the perimeter and the length of the rectangle

✪ Perimeter of a rectangle = 2( length + breadth) or 2 times the sum of length and breadth .

➠ Perimeter of the rectangle = 2( l + b)

➠ 80cm = 2( 22 + b)

➠ 80cm = 44 + 2 × breadth

➠ 2 × breadth = 80 - 44

➠ 2 × breadth = 36

➠ breadth = 36 / 2

➠ breadth = 18cm

• Therefore, the breadth of the rectangle is 18cm

~ Now, let's find the area of the square using the given concepts and substituting the value of 20cm as the side

✪ Area of a square = side times side

➠ Area of the square = side × side

➠ Area of the square = 20 × 20

➠ Area of the square = 400cm²

• Therefore the area of the square = 400cm²

~Now, let's find the area of the rectangle using the measurement of length which we found and the measurement of breadth already mentioned in question above.

✪ Area of a rectangle = length times breadth

➠ Area of the rectangle = length × breadth

➠ Area of the rectangle = 22 × 18

➠ Area of the rectangle = 396cm²

• Therefore the area of the rectangle is 396cm²

➽ Now, Let's compare the area's of the square

and the rectangle so, that we can state which has the greater area.!

Hence:

• The area enclosed by the square is more than the rectangle

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${ \large{ \underline{ \pmb{ \frak{ Diagrams : }}}}}$

❍ Square:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 20\ cm}\put(4.4,2){\bf\large 20\ cm}\end{picture}$

❍ Rectangle:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 22 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 18 cm}\end{picture}$

[Note : kindly see the diagrams from the web if you need the diagrams too]

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Answer 2

Answer:

Step-by-step explanation: