Question

A wire is bent to form a rectangle of 28 m x 10 m. It is again straightened and bent now to form a square. What is the side of the square so formed?
Please answer this urgent

Answer 1

19m will be the answer sure

Answer 2

Given:

• A wire is bent to form a rectangle of 28m×10m.

• It is again straightened and bent now to form a square

To Find:

• What is the side of the square so formed?

Solution:

→ Here, it is given that the wire which was bent to from a rectangle is made to from a square. As the same wire is used so, we know that

• perimeter of rectangle = perimeter of square

→ Now, let's find the perimeter of the rectangle and then find the side of the square.

${ \purple{ \underline{ \frak{ \dag \: As \: we \: know \: that \: }}}}$

${\longrightarrow}\blue{ \underline{ \boxed{ \pink{ \mathfrak{ \: perimeter \: of \: a \: rectangle = 2(l + b)}}}}\bigstar}$

→ Lets substitute the dimensions now:

$\longrightarrow \tt \: perimeter \: of \: the \: rectangle = 2(l + b) \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: perimeter \: of \: the \: rectangle = 2(28 + 10) \\ \\ \\ \longrightarrow \tt \: perimeter \: of \: the \: rectangle = 2 \times 38 \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: perimeter \: of \: the \: rectangle = \orange{ \underline{ \boxed{ \mathfrak{ 76m}} \bigstar}} \: \: \: \: \: \:$

${ \pink{ \underline{ \frak{Hence \: The \: Perimeter \: of \: thr \: Rectangle \: is \: 76m}}}}$

→ We Know, perimeter of the rectangle and the square are the same so, perimeter of the square is 76m

→ Now, let's find Its side:

${ \blue{ \underline{ \frak{As \: we \: know \: that : }}}}$

${\longrightarrow}\blue{ \underline{ \boxed{ \pink{ \mathfrak{perimeter \: of \: the \: square = 4 \times side}}} \bigstar}}$

→ Lets substitute the values now :

$\longrightarrow \tt \: perimeter = 4 \times side \\ \\ \\ \longrightarrow \tt \: 76 = 4 \times side \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: side = \cancel \frac{76}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: side = \blue{ \underline{ \boxed{ \frak{19m}}} \bigstar} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${ \pink{ \underline{ \frak{Hence \: The \: side \: of \: the \: square = 19m}}}}$

Diagram:

Square:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){4}}\multiput(0,0)(0,4){2}{\line(1,0){4}}\put(-0.5,-0.5){\bf D}\put(-0.5,4.2){\bf A}\put(4.2,-0.5){\bf C}\put(4.2,4.2){\bf B}\put(1.5,-0.6){\bf\large 19\ cm}\put(4.4,2){\bf\large 19\ cm}\end{picture}$

Rectangle:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 28 m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 10 m}\end{picture}$

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