Question

the area of a square and rectangle are equal. if the side of the square is 50cm and breadth of the rectangle is 30cm, find the length and perimeter of the rectangle.​

Answer 1

Answer :

• Length of rectangle = 83.3 cm
• Perimeter of rectangle = 226.6 cm

Given that :

• The area of square and rectangle are equal
• If the side of the square is 50cm and the breadth of rectangle is 30cm

To find :

• Length of rectangle
• Perimeter of rectangle

Solution :

We know that,

• Area of square = a²

where,

• a is side (50cm)

⟿ Area of square = (a)² = (50)² = 2500cm

• Area of square = 2500cm
• Breadth of rectangle = 30cm

Finding the length of rectangle

• let the length of rectangle be l

We know that,

• Area of rectangle = l × breadth

⟿ length × 30

According to question, Given that , the area of square and rectangle are equal so,

• Area of square = Area of rectangle

⟿ 2500 = l × 30

⟿ l = 2500/30

⟿ l = 83.3 cm

Length of rectangle is 83.3 cm

Finding the perimeter of rectangle :

we know that,

• Perimeter of rectangle = 2(l + b)

Where,

• l is length of rectangle
• b is breadth of rectangle

⟿ Perimeter of rectangle = 2(length + breadth)

⟿ 2(83.3 + 30)

⟿ 2(113.3)

⟿ 226.6 cm

Perimeter of rectangle is 22.6cm

Hence,

• Length of rectangle = 83.3 cm
• Perimeter of rectangle = 226.6cm

Answer 2

Given:-

• The Area of Square and Rectangle are equal.

• Side of the square = 50cm

• Breadth of the rectangle = 30cm.

To find:-

• Length of rectangle

• Perimeter of rectangle

Formula Used:-

• ${\boxed{\bf{Area\: of\: square\: = a^2}}}$

• ${\boxed{\bf{Area \:of\: rectangle = Length \times breadth}}}$

• ${\boxed{\bf{Perimeter \:of\: rectangle =2(l+b)}}}$

Solution:-

Firstly Using Formula,

$\sf :\implies\:Area\: of\: square\: = a^2$

$\sf :\implies\:Area\: of\: square\: = 50^2$

$\sf :\implies\:Area\: of\: square\: = 2500\:cm^2$

According to question,

$\sf :\implies\:Area\: of\: Rectangle\: = Area\: of\: Square$

$\sf :\implies\: Length \times Breadth= 2500$

$\sf :\implies\: Length \times 30= 2500$

$\sf :\implies\: Length = \dfrac{2,500}{30}$

$\sf :\implies\: Length = \dfrac{2,50}{3}$

$\sf :\implies\: Length = 83.33\:cm$

Now,

$\sf :\implies\: Perimeter\:of\: Rectangle=2(l+b)$

$\sf :\implies\: Perimeter\:of\: Rectangle=2(83.33+30)$

$\sf :\implies\: Perimeter\:of\: Rectangle=2\times 113.33$

$\sf :\implies\: Perimeter\:of\: Rectangle=226.66\:cm$

Hence, The Length and Perimeter of the rectangle is 83.33cm and 226.66cm respectively.

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