Question

The area of a square and rectangular are equal. If the side of the
square is 40 cm and the breadth of the rectangle is 25 cm, find the
length of the rectangle. Also find the perimeter of the rectangle.

Answer 1

GivEn:

• Area of square = Area of Rectangle
• Side of square = 40 cm
• Breadth of rectangle = 25 cm

To find:

• Length of Rectangle?
• Perimeter of Rectangle?

Solution:

☯ Let Length of rectangle be x cm.

★ According to the Question:

Area of square = Area of rectangle

➯ 40 × 40 = 25 × x

➯ 1600 = 25x

➯ x = 1600/25

➯ x = 64 cm

Thus, Length of rectangle is 64 cm.

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Now, Finding Perimeter of rectangle,

We know that,

★ Perimeter of rectangle = 2(l + b)

Here,

• Length, l = 64 cm
• Breadth, b = 25 cm

Therefore,

➯ Perimeter = 2(64 + 25)

➯ Perimeter = 2(89)

➯ Perimeter = 2 × 89

➯ Perimeter = 178 cm

Hence, Perimeter of rectangle is 178 cm.

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⠀⠀⠀⠀★ Formulas related to it :

• Perimeter of square = 4 × side
• Area of Square = side × side
• Perimeter of rectangle = 2(l + b)
• Area of Rectangle = Length × breadth
• Diagonal of square = √2 a
• Diagonal of rectangle = √l² + b²

Answer 2

Answer:

Given :-

• The area of a square and rectangle are equal.
• The side of the square is 40 cm and the breadth of the rectangle is 25 cm.

To Find :-

• What is the length and perimeter of the rectangle.

Formula Used :-

To find perimeter of the rectangle we know that,

$\boxed{\bold{\small{Perimeter\: =\: 2(Length\: +\: Breadth)}}}$

Solution :-

Let, the length of the rectangle be x

According to the question,

⇒ 25 × x = (40)²

⇒ 25x = 1600

⇒ x = $\sf\dfrac{\cancel{1600}}{\cancel{25}}$

➠ x = 64 cm

$\therefore$ The length of the rectangle is 64 cm .

Now, we have to find the perimeter of the rectangle,

Given :

• Length (l) = 64 cm
• Breadth (b) = 25 cm

According to the question by using the formula we get,

⇒ Perimeter = 2(length + breadth)

⇒ Perimeter = 2(64 + 25)

⇒ Perimeter = 2(89)

➠ Perimeter = 178 cm

$\therefore$ The perimeter of the rectangle is 178 cm .