Question

A rectangular field and a square field have a perimeter of 36 m each. Which field hos the largest area if the length of the rectangle is 12 m?​

Answer 1

Step-by-step explanation:

First let's take square.

So first of all we will take out its side.

Side of square = Perimeter / 4

                        = 36/4

                        = 9 m

Now we'll find the area of square.

Area of square = 4 × side

                         = 4 × 4

                         = 16 m sq

Now secondly let's take rectangle.

As we are given with length so we'll find the breadth by forming equation.

Perimeter = 2 ( l + b )

36 = 2 (12 + b)

36/2 = 12 + b

18  = 12 + b

18 - 12 = b

6 m = b

Now we will find the area.

Area of rectangle = l × b

                             = 12 × 6

                             = 72 m sq

Area of Square = 16 m sq

Area of Rectangle = 72 m sq

                   = 72 > 16

Therefore, Rectangle has the bigger area.

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Answer 2

Answer:

the square field has the largest area .

Step-by-step explanation:

Let the length of width of the rectangular field = a m

perimeter of the rectangle = 2(12+a) m

According to question ,

2(12 + a) = 36

⇒ 12 + a = 18

⇒ a = 6

area of the rectangle = 12×6 = 72 m^2

let length of one side of the square = r m.

then perimeter of the square is 4r m

according to question , 4r = 36

⇒ r = 9

therefore area of the square is 9^2 = 81 m^2

81 > 72

Hence area of the square field is largest .