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The area of a square field is 5184 m2 . Find the area of a rectangular field, whose perimeter is equal to the perimeter of the square field, and whose length is twice of its breadth.

The area of a square field is 5184 m2
. Find the area of a rectangular field, whose perimeter is equal to the perimeter of the square field, and whose length is twice of its breadth.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
19 days ago
Hint: Here, we need to find the area of the rectangular field. First, we will find the side of the square and its perimeter. Using the formula for the perimeter of a rectangle, we can find the dimensions of the rectangle. Finally, we will substitute the value of dimensions of the rectangle in the formula for the area of a rectangle to find the area of the rectangular field. Formula Used: We will use the following formulas: 1.The area of a square is given by the formula s2 , where s is the length of the side of the square. 2.We will use the formula Area of rectangle =l×b , where l is the length of the rectangle and b is the breadth of the rectangle. Complete step-by-step answer: First, we will find the side of the square. The area of a square is given by the formula s2 , where s is the length of the side of the square. It is given that the area of a square field is 5184 m2 . Therefore, we get 5184=s2 Taking the square root of both sides, we get ⇒s=72 m Thus, the side of the square is of length 72 m. Now, we will find the perimeter of the square. Substituting s=72 m in the formula for perimeter of a square, we get ⇒ Perimeter =4×72 Multiplying the terms, we get ⇒ Perimeter =288 m Let the breadth of the rectangular field be x . It is given that the length of the rectangular field is twice its breadth. Therefore, we get ⇒ Length of rectangular field =2x Substituting breadth as x and length as 2x in the formula for perimeter of a rectangle, we get ⇒ Perimeter =2(2x+x) Adding the like terms in the parentheses, we get ⇒ Perimeter =2(3x) Multiplying the terms in the expression, we get ⇒ Perimeter =6x It is given that the perimeter of the square and rectangular field is the same. Therefore, we get the equation ⇒ 6x=288 This is a linear equation in one variable. We will solve this to find the value of x . Dividing both sides of the equation by 6, we get ⇒ x=48 Therefore, the breadth of the rectangular field is 48 m. Substituting x=48 m in the expression 2x , we get ⇒ Length of rectangular field =2×48=96 m Finally, we will calculate the area of the rectangular field. The area of a rectangle is the product of its length and breadth. Therefore, we get ⇒ Area of rectangular field =96×48 Multiplying the terms in the expression, we get ⇒ Area of rectangular field =4608m2 Thus, we get the area of the rectangular field as 4608 m2 . Note: We have formed a linear equation in one variable in terms of x in the solution. A linear equation in one variable is an equation of the form ax+b=0 , where a and b are integers. A linear equation of the form ax+b=0 has only one solution. We used the formula for the perimeter of a square and rectangle in the solution. The perimeter of a square of side s is given as 4s . The perimeter of a rectangle with length l and breadth b is given as 2(l+b) .

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