Question

A square and a rectangle have the same perimeter. Calculate the area of the rectangle if the side of the square is 60 cm and the length of the rectangle is 80 cm.​

Answer 1

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Perimeter of square formula = 4 × side of the square

Hence,

➠P (square) = 4 × 60 = 240 m

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Perimeter of rectangle formula = 2 × (Length + Breadth)

Hence,

➠P (rectangle) = 2 (80 + Breadth) = 160 + 2 × Breadth

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According to the given question,

➩160 + 2 × Breadth = 240

➩2 × Breadth = 240 – 160

➩Breadth = 80/2

➩Breadth of the rectangle = 40 m

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⇝Now, the area of rectangle = Length × Breadth = 80 × 40 = 3200m²

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Answer 2

Given,

The perimeter of a square = perimeter of a rectangle

Each side of the square = A = 60 centimeters

Length of the rectangle = L =80 centimeters

To find,

The area of the rectangle.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the breadth of the rectangle is "B" centimeters.

As per the concepts of mensuration,

The perimeter of a rectangle

= perimeter (rectangle)

= 2 x (Length + Breadth)

= 2 x (L + B)

The perimeter of a square

= perimeter (square)

= 4 x (length of each side)

= 4 x A

The area of a rectangle

= Area (rectangle)

= L x B

Now, as per the question,

The perimeter of rectangle = The perimeter of the square

=> perimeter (rectangle) = perimeter (square)

=> 2 x (L + B) = 4 x A

=> 2 x (80 + B) = 4 x 60

=> B + 80 = 120

=> B = 40 centimeters

So, the area of the rectangle is

= Length x Breadth = L x B

= (80x40) square centimeters

= 3,200 square centimeters

Hence, the area of the rectangle is 3,200 square centimeters.