Q. 14.2( 330 Votes )

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?


Answer :

Given:
Length of rectangle = l = 80 cm
side of square = a = 60 cm

Also, we know
Perimeter of rectangle = 2(l + b)
Area of rectangle = lb,
where l = length and b = breadth

Perimeter of square = 4a
area of square = a2  ,
where a is side of square.
Let breadth of the rectangle be b

Perimeter of the rectangle = Perimeter of the square


2 × (80 + b) = 4 × 60
2 × (80 + b) = 240

(80 + b) = 240/2
80 + b = 120

b = 120 - 80

b = 40 m


Now, area of square = a2 = 602 = 3600 m2


And area of the rectangle = lb = 80 × 40 = 3200 m2


Clearly, area of square is greater.

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