Question

The perimeterof a rectangle is equal to the parameter of a square if the length and with rectangle is 20 and 10 respectively find the area of the square.​

Answer 1

Answer:

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

It is given that the perimeter of rectangle is equal to perimeter of square . We have to calculate the area of square . So Let's start ,

• Length of Rectangle ,l = 20
• Breadth of Rectangle ,b = 10

Let the side of square be x

☯ Perimeter of Rectangle = Perimeter of Square

$:\implies$ 2(l+b) = 4 × side

$:\implies$ 2(20+10) = 4 × x

$:\implies$ 2(30) = 4×x

$:\implies$ 60 = 4x

$:\implies$ 60/4 = x

$:\implies$ x = 60/4

$:\implies$ x = 15

So, the side of square is 15 units .

Now, calculating the area of square.

☯ Area of Square = (Side)²

Substitute the value we get

$:\implies$ Area of Square = 15²

$:\implies$ Area of Square = 225 sq.units

• Hence, the area of square is 225 sq. units .

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Answer 2

Answer:

Appropriate Question :-

• The perimeter of a rectangle is equal to the perimeter of a square if the length and the width of a rectangle is 20 and 10 respectively. Find the area of the square.

Given :-

• The perimeter of a rectangle is equal to the perimeter of a square if the length and width of a rectangle is 20 and 10 respectively.

To Find :-

• What is the area of the square.

Formula Used :-

$\clubsuit$ Perimeter of Rectangle :

$\longmapsto \sf\boxed{\bold{\pink{Perimeter\: of\: Rectangle =\: 2(Length + Breadth)}}}$

$\clubsuit$ Perimeter of Square :

$\longmapsto \sf\boxed{\bold{\pink{Perimeter\: of\: Square =\: 4a}}}$

where,

• a = Side

$\clubsuit$ Area of Square :

$\longmapsto\sf\boxed{\bold{\pink{Area\: of\: Square =\: (a)^2}}}$

where,

• a = Side

Solution :-

First, we have to find the side of a square :

Let,

$\mapsto$ Side of Square = y units

Given :

• Length = 10 units
• Breadth = 20 units

According to the question by using the formula we get,

$\implies \sf 2(10 + 20) =\: 4(y)$

$\implies \sf 20 + 40 =\: 4y$

$\implies \sf 60 =\: 4y$

$\implies \sf \dfrac{\cancel{60}}{\cancel{4}} =\: y$

$\implies \sf 15 =\: y$

$\implies \sf\bold{\green{y =\: 15\: units}}$

Hence, the side of square is 15 units.

Now, we have to find the area of square :

Given :

• Side of Square = 15 units

According to the question by using the formula we get,

$\dashrightarrow \sf Area\: of\: Square =\: {(15)}^{2}$

$\dashrightarrow \sf Area\: of\: Square =\: 15 \times 15$

$\dashrightarrow \sf\bold{\red{Side\: of\: Square =\: 225\: sq.units}}$

$\therefore$ The area of square is 225 sq.units .