The area of a square field is 5184 m². Find the area of a rectangular field, whose perimeter
is equal to the perimeter

2 thoughts on “<br />The area of a square field is 5184 m². Find the area of a rectangular field, whose perimeter<br />is equal to the perimeter”

1. Answer:

   4608m²

   Step-by-step explanation:

   Here,

   Area of square field is 5184m².

   ⇒Let each side of square be p m.

   Now,

   We know that,

   ⇒Area of Square = a x a

   So,

   ⇒ 5184 = p²

   ⇒ p =√5184

   ⇒ p = 72 m

   ∴ Each side of square is 72m.

   ⇒Perimeter of Square = 4a

   = 4(72)

   = 288

   ∴ Perimeter of square is 288 m.

   Now,

   ⇒We are given that length of rectangular field is twice it’s breadth.

   ⇒Let it’s breadth be x m.So its length will be 2x m.

   ⇒We are also given that perimeter of given square field is equal to perimeter of rectangle.

   ∴Perimeter Of Square = Perimeter of Rectangle

   ⇒ 288 = 2( l + b ) ∵area of rectangle = 2 (l + b)

   ⇒ 288 = 2 ( 2x + x) ∵ l = 2x and b = x

   ⇒ 288/2 = 2x + x

   ⇒ 144 = 3x

   ⇒ x = 144/3

   ⇒ x = 48.

   ∴ breadth of rectangle = b = x = 48m.

   &

   length of rectangle = l = 2x = 2(48) = 96m.

   Now,

   We need to find area of rectangular feild.

   So,

   ⇒Area of rectangle = l x b

   ⇒Area of rectangular field = 48 x 96

   ⇒Area of rectangular field = 4608

   ∴ The area of required rectangular field is 4608m².

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2. Step-by-step explanation:

   Area of square=5184m square

   Area formula of square=side x side

   So,side of square is square root of 5184=72cm

   Perimeter of rectangle=Perimeter of square

   So,

   Perimeter of square=4xside=4×72=288m

   Length of rectangle=2x breadth

   Perimeter of rectangle=2(l+b)=288m

   l=2b so, 2(2b+b)=288m

   2(3b)=288m

   3b=144m

   b=144/3=48m

   l=2b so, l=2×48=96m

   b=48m and l= 96m

   So, area of rectangle=lxb=96×48=4608 m square.

   Hope it’s the correct answer

   Hope it helped 🙂

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