Question

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

Ans: GIVEN: 60 m side of square
80m length of rectangle
TOFIND: which field has a larger area?
SOLUTION:
perimeter of Square = perimeter of rectangle
4×side = perimeter of rectangle
4×6 = perimeter of rectangle
Therefore,
240m = perimeter of rectangle

hence, perimeter of rectangle = 240m
perimeter of rectangle = 2(l+b)
240 = 2(80+b)
240/2 = 80+b
120 = 80+b
breadth = 120-80
therefore, breadth = 40m
Area of rectangle = l×b
= 80×40
area of rectangle = 3200 m²

Area of square = side²
= 60²
area of squares = 3600m²

THEREFORE, area of square is larger than area of rectangle.

AREA OF SQUARE >AREA OF RECTANGLE.
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Answer 1

You yourself have solved your question

Answer 2

Answer:

Let the side of square field be a=60 m

Let the length of the rectangular field be l=80 m and breadth be b m.

According to the question

perimeter of square = Perimeter of rectangle

4×a=2(l+b)

⇒4×60=2(80+b)

⇒240=160+2b

⇒2b=80

⇒b=40

Area of square =60×60=3600m

2

Area of rectangle=80×40=3200m

2

So, the area of the square is greater than the area of the rectangle.