Question

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

Answer 1

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=3600m2

Area of rectangle=80×40=3200m2

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

Answer 2

Let the side of square be a=60m

ATQ,

perimeter of square =perimeter of rectangle

$= 4 \times a = 2(l + b) \\ \\ = 4 \times 60 = 2(80 + b) \\ \\ 240 = 160 + 2b \\ \\ 2b = 80 \\ \\ \therefore \: b = \frac{ \cancel{ {80}} \: \: ^{40} }{ \cancel2}$

=40m

Area of square

$= 60 \times 60 = 3600 {m}^{2}$

Area of rectangle

$= 80 \times 40 = {3200m}^{2}$

So area of square is greater than area of rectangle