Question

Q-7 The area of a square of side 6 cm is same as that of a rectangle of length
12 cm. What is the breadth of the rectangle?​

Answer 1

$\begin{gathered}\begin{gathered}\bf \: Given \:  - \begin{cases} &\sf{side \: of \: square \: = 6 \: cm} \\ &\sf{length \: of \: rectangle \: = \: 12 \: cm}\\ &\sf{Area_{(square)} \: = \: Area_{(rectangle)}} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\:find - \begin{cases} &\sf{Breadth \: of \: rectangle}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline{\bold{Solution-}}$

We know,

$\boxed{ \bf \: Area_{(rectangle)} = Length \times Breadth}$

and

$\boxed{ \bf \: Area_{(square)} = {(side)}^{2} }$

Now,

Given that

• Side of square = 6 cm

So,

$\rm :\longmapsto\:\bf \: Area_{(square)} = {(side)}^{2}$

$\rm :\longmapsto\:Area_{(square)} = {6}^{2}$

$\rm :\longmapsto\:Area_{(square)} = 36 \: {cm}^{2} - - (1)$

Also,

• Length of rectangle = 12 cm

• Let Breadth of rectangle be 'x' cm

So,

$\rm :\longmapsto\: \bf \: Area_{(rectangle)} = Length \times Breadth$

$\rm :\longmapsto\:Area_{(rectangle)} = 12 \times x$

$\rm :\longmapsto\:Area_{(rectangle)} = 12x \: {cm}^{2}$

Now,

$\large\underline{\bold{According \: to \: statement-}}$

$\rm :\longmapsto\:Area_{(rectangle)} = Area_{(square)}$

On substituting the values from equation (1) and (2), we get

$\rm :\longmapsto\:12x = 36$

$\rm :\longmapsto\:x = 3 \: cm$

$\boxed{\bf\implies \: Breadth \: of \: rectangle \: = \: 3 \: cm}$

Additional Information :-

$(1). \: \boxed{ \tt{Perimeter_{(rectangle)} = 2(Length + Breadth)}}$

$(2). \: \boxed{ \tt{Perimeter_{(square)} = 4 \times side}}$

$(3). \: \boxed{ \tt{Area_{(square)} = \dfrac{1}{2} {(diagonal)}^{2} }}$

$(4). \: \boxed{ \tt{diagonal_{(rectangle)} = \sqrt{ {Length}^{2} + {Breadth}^{2} } }}$

$(5). \: \boxed{ \tt{diagonal_{(square)} = \sqrt{2} \times side}}$