Question

please answer me with solution please it's a humble request​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the concept of Area of Square has been used. Firstly we shall assume the side of initial square as a variable. Then we shall find its area. After that we shall make increase in side of the square by 50% and then find the area of square with new side. Then we shall find the percentage increase in area of final square.

Let's do it !!

________________________________________________

★ Formula Used :-

$\\\;\boxed{\sf{\pink{Area\;of\:Square\;=\;\bf{(Side)^{2}}}}}$

$\\\;\boxed{\sf{\pink{\%\;increase\;in\;Area\;=\;\bf{\dfrac{Final_{(Area)}\;-\;Initial_{(Area)}}{Initial_{(Area)}}\;\times\;100\;\%}}}}$

________________________________________________

★ Solution :-

» Increase in side = 50%

• Let the initial side of square be x

• Let the initial area of square be A

• Let the final side of square be x + (50% + x)

• Let the final area of square be A'

» Initial Area shows area with initial side.

» Final Area shows area with increased side.

________________________________________________

~ For Area of square with initial side ::

• Side of square = x

Then area of square is given as,

$\\\;\sf{:\rightarrow\;\;Area\;of\:Square\;=\;\bf{(Side)^{2}}}$

Now by applying values, we get

$\\\;\sf{:\rightarrow\;\;Area\;of\:Square_{(Initial)}\;=\;\bf{(x)^{2}}}$

$\\\;\bf{:\rightarrow\;\;Area\;of\:Square_{(Initial)}\;=\;\bf{\orange{x^{2}}}}$

________________________________________________

~ For Area of square with increased side ::

We know that increase in side is by 50%

So,

$\\\;\tt{\rightarrow\;\;Increase\;in\;side\;=\;\bf{x\;+\;\bigg(50\%\;+\;x\bigg)}}$

$\\\;\tt{\rightarrow\;\;Increase\;in\;side\;=\;\bf{x\;+\;\bigg(\dfrac{50}{100}\;+\;x\bigg)}}$

$\\\;\tt{\rightarrow\;\;Increase\;in\;side\;=\;\bf{x\;+\;\bigg(\dfrac{1}{2}\;\+\;x\bigg)}}$

$\\\;\tt{\rightarrow\;\;Increase\;in\;side\;=\;\bf{x\;+\;\dfrac{x}{2}}}$

$\\\;\tt{\rightarrow\;\;Increase\;in\;side\;=\;\bf{\dfrac{2x\;+\;x}{2}}}$

$\\\;\bf{\rightarrow\;\;Increase\;in\;side\;=\;\bf{\red{\dfrac{3x}{2}}}}$

• Area of the square with increased side :

We know that,

$\\\;\sf{:\rightarrow\;\;Area\;of\:Square\;=\;\bf{(Side)^{2}}}$

Now by applying values, we get

$\\\;\sf{:\rightarrow\;\;Area\;of\:Square_{(Final)}\;=\;\bf{\bigg(\dfrac{3x}{2}\bigg)^{2}}}$

$\\\;\bf{:\rightarrow\;\;Area\;of\:Square_{(Final)}\;=\;\bf{\blue{\dfrac{9\:x^{2}}{4}}}}$

________________________________________________

~ For % increase in area of square ::

We know that,

$\\\;\sf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{\dfrac{Final_{(Area)}\;-\;Initial_{(Area)}}{Initial_{(Area)}}\;\times\;100\;\%}}$

Now by applying values, we get

$\\\;\sf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{\dfrac{\bigg(\dfrac{9\:x^{2}}{4}\bigg)\;-\;x^{2}}{x^{2}}\;\times\;100\;\%}}$

$\\\;\sf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{\dfrac{\bigg(\dfrac{9\:x^{2}\;-\;4\:x^{2}}{4}\bigg)}{x^{2}}\;\times\;100\;\%}}$

$\\\;\sf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{\dfrac{\bigg(\dfrac{5\:x^{2}}{4}\bigg)}{x^{2}}\;\times\;100\;\%}}$

$\\\;\sf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{\dfrac{5\:x^{2}}{4\:x^{2}}\;\times\;100\;\%}}$

Cancelling x², we get

$\\\;\sf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{\dfrac{5}{4}\;\times\;100\;\%}}$

$\\\;\sf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{5\:\times\:25\;\%}}$

$\\\;\bf{:\Longrightarrow\;\;\%\;increase\;in\;Area\;=\;\bf{\purple{125\;\:\%}}}$

$\\\;\underline{\boxed{\tt{Required\;\:\%\;increase\;\:in\;\:Area\;=\;\bf{\purple{125\;\:\%}}}}}$

________________________________________________

★ More to know :-

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Square\;=\;4\:\times\:Side}$

$\\\;\sf{\leadsto\;\;Diagonal\;of\;square\;=\;(Side)\sqrt{2}}$

• Properties of Square ::

• It is a type of Parallelogram.

• Opposite sides are equal and parallel.

• All the angles of square are 90°

• Diagonals of square bisect each other at 90°

• All the sides of square are equal.

Answer 2

Here the concept of Area of Square has been used. Firstly we shall assume the side of initial square as a variable. Then we shall find its area. After that we shall make increase in side of the square by 50% and then find the area of square with new side. Then we shall find the percentage increase in area of final square.

★ Solution :-

★ Solution :-» Increase in side = 50%

★ Solution :-» Increase in side = 50%Let the initial side of square be x

★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be A

★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)

★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'

★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side.

★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side.

★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side. • Properties of Square ::

★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side. • Properties of Square ::It is a type of Parallelogram.

• ★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side. • Properties of Square ::It is a type of Parallelogram.Opposite sides are equal and parallel.
• ★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side. • Properties of Square ::It is a type of Parallelogram.Opposite sides are equal and parallel.All the angles of square are 90°
• ★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side. • Properties of Square ::It is a type of Parallelogram.Opposite sides are equal and parallel.All the angles of square are 90°Diagonals of square bisect each other at 90°
• ★ Solution :-» Increase in side = 50%Let the initial side of square be xLet the initial area of square be ALet the final side of square be x + (50% + x)Let the final area of square be A'» Initial Area shows area with initial side. • Properties of Square ::It is a type of Parallelogram.Opposite sides are equal and parallel.All the angles of square are 90°Diagonals of square bisect each other at 90°All the sides of square are equal.