Question

if length and breadth of a rectangle became half and double repectively then what will be the percentage increase crease in resultant area?​

Answer 1

Let length of original rectangle = x

Let Breath of original rectangle = y

Area of the rectangle = length × Breath

= xy

According to the question:

length of second rectangle = x/2

Breath of second rectangle = 2y

Area of the rectangle = length × Breath

$\rm\implies \dfrac{x}{2} \times 2y$

$\rm\implies \dfrac{x}{\not{2}} \times \not{2}y$

$\rm\implies xy$

Area of first rectangle = Area of second rectangle

Area increased = xy - xy = 0

$\underline{\boxed{\rm Increse\% = \dfrac{increase}{original\: value}\times 100}}$

$\implies\rm\dfrac{0}{xy}\times 100$

$\implies\rm 0 \%$

Percentage of area increased = 0%

Answer 2

$\large{\boxed{\boxed{\sf Let's \: Understand \: Question \: F1^{st}}}}$

Here, we have said that the Length and Breadth of a rectangle is halved and doubled respectively. Then, what will be the increase in the area of the Rectangle.

$\large{\boxed{\boxed{\sf How \: To \: Do \: It?}}}$

Here, f1st we find the area of rectangle before the length and breadth is halved and doubled. The find the area of rectangle after the length and breadth is halved and doubled. Then, we will compare the area in both conditions and will got our required answer.

$\huge{\underline{\boxed{\sf AnSwer}}}$

_____________________________

Given:-

• Length and Breadth of rectangular is halved and doubled respectively.

Find:-

• Percentage increase in the resultant area.

Solution:-

Let, the Length of rectangle be ❛L❜ units

Let, Breadth of rectangle be ❛B❜ units

Now, using

$\begin{lgathered} \\ :\implies \: \: \: \: \underline{\boxed{\sf Area \: of \: rectangle = l \times b}} \\ \\ \end{lgathered}$

$\begin{lgathered} \\ :\to \sf Area \: of \: rectangle = LB \: sq. \: units\\ \\ \end{lgathered}$

❍ Length and Breadth of Rectangle is halved and doubled respectively.

➟ Length = L/2 units

➟ Breadth = 2B units

Now, again using

$\begin{lgathered} \\ :\implies \: \: \: \: \underline{\boxed{\sf Area \: of \: rectangle = l \times b}} \\ \\ \end{lgathered}$

$\begin{lgathered} \\ :\to \sf Area \: of \: rectangle = \dfrac{L}{2} \times 2B\\ \\ \end{lgathered}$

$\begin{lgathered} \\ :\to \sf Area \: of \: rectangle = \dfrac{L}{ \not2} \times \not2B\\ \\ \end{lgathered}$

$\begin{lgathered} \\ :\to \sf Area \: of \: rectangle = LB \: sq. \: units\\ \\ \end{lgathered}$

Here,

Area of rectangle before changes = Area of rectangle after changes

➢ Area increased = Area before changes - Area after changes = LB - LB = 0

no, using

$\begin{lgathered} \\ :\implies \: \: \: \: \underline{\boxed{\sf Percentage = \dfrac{increase\:area}{Real\: area}\times 100}} \\ \\ \end{lgathered}$

$\begin{lgathered} \\ :\to \sf Percentage = \dfrac{0}{LB}\times 100\\ \\ \end{lgathered}$

$\begin{lgathered} \\ :\to \sf Percentage = 0\times 100\\ \\ \end{lgathered}$

$\begin{lgathered} \\ :\to \sf Percentage = 0\%\\ \\ \end{lgathered}$

$\underline{\boxed{\sf \therefore Percentage\: increased\:in\: resultant\: area\:is \: 0\%}}$