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

EXPLANATION.

Square and rectangle have same perimeter.

=> Sides of square is = 60 cm.

=> Length of the rectangle is = 80 cm.

perimeter of square = 4 X ( sides of square)

=> 4 X 60 = 240 m. ...... (1)

perimeter of rectangle = 2 X ( L + B )

=> 2 X ( 80 + B)

=> 160 + 2B ......(2)

=> 160 + 2B = 240

=> 2B = 240 - 160

=> 2B = 80

=> B = 40 m.

Area of rectangle = L X B.

=> 80 X 40 = 3200 m².

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.