Question

the length and breath of a rectangle is 9 m 7 m respectively if the perimeter of the square is same as perimeter of rectangle find the area of square

Answer 1

Answer:

$\bigstar{\bold{Area\:of\:square=64\:m}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Length of the rectangle = 9 m
• Breadth of the rectangle = 7 m
• Perimeter of square = Perimeter of rectangle

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Area of the square

$\Large{\underline{\underline{\bf{Solution:}}}}$

➦ First we have to find the perimeter of the rectangle.

➦ Perimeter of a rectangle is given by,

    Perimeter of rectangle =  2(l + b)

    where l = length

    b = breadth

➦ Substitute the data,

    Perimeter of the rectangle = 2 (9 + 7)

    Perimeter of the rectangle = 2 × 16

    Perimeter of the rectangle = 32 m

➦ Hence the perimeter of the rectangle is 32 m

➦ But by given,

    Perimeter of square = Perimeter of rectangle

➦ Hence,

    Perimeter of square = 32 m

➦ Now we have to find the side of the square.

➦ Perimeter of a square is given by,

   Perimeter of square = 4 a

    where a is a side of the squuare

➦ So,

    4a = 32

      a = 32/4

      a = 8

➦ Hence side of the square is 8 m

➦ Now area of a square is given by,

    Area of square = a²

➦ Substitute the data,

    Area of square = 8²

    Area of square = 64 m²

➦ Hence area of the square is 64 m²

    $\boxed{\bold{Area\:of\:square=64\:m}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

➦ Perimeter of a rectangle  = 2 (l + b)

➦ Area of a rectangle = l × b

➦ Perimeter of a square = 4a

➦ Area of a square = a²

Answer 2

Answer :-

✒ $\large{\bold{Area\: of\: the\: square}} = \bold{64\: m^{2}}$

$\rule{300}{1}$

★ Concept :-

Here the concept of areas and perimeter of Rectangle and Square has been used. According to this, the given are the formulas :-

• Area of Rectangle = Length × Breadth

• Area of Square = (Side)²

• Perimeter of Rectangle = 2(Length + Breadth)

• Perimeter of Square = 4 × side

$\rule{300}{1}$

★ Solution :-

Given,

• Length of rectangle, L = 9 m

• Breadth of rectangle, B = 7 m

• Perimeter of Rectangle = Perimeter of Square

Then,

✒Perimeter of Rectangle = 2(L + B)

$By \: applying \: the \: values \: we\: get,$

✒Perimeter of Rectangle = 2(9 + 7)

✒ Perimeter of Rectangle = 2 × 16

✒ Perimeter of Rectangle = 32 m

We know that, Perimeter of Rectangle = Perimeter of Square. Then,

✒ Perimeter of Square = 32 m

✒ 4 × side = 32 m

✒$\bold{Side} \: = \: \bold{\dfrac{32}{4}}$

✒ Side = 4 m

Hence, side of the square = 4 m

Now let us find the area of the square,

✏ Area of the square = (side)²

✏ Area of the square = (8)²

✏ Area of the square = 64 m²

Hence, the area of the square =

64 m².

___________________

★ More to know :-

• Square is a two dimensional figure with four closed sides perpendicular to each other with equal length. Its diagonals also are equal.

• Rectangle is also a two dimensional four sided closed figure with all the sides perpendicular to each other where opposite sides are equal to each other. Diagonals are equal and bisect each other.

• Parallelogram is a four sided 2 D figure where opposite sides are parallel to each other.

• Rhombus is a four sided closed 2 D figure where all the sides are equal and diagonals are not equal.