A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?a)65b)78c)82d)89e)None of the AboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given that area of rectangular field and and one side of the rectangle so so by using the area formula of the rectangle we can find the other side of the rectangle and he also told that only with 3 sides of the rectangle has been covered with the friends so by adding two breadth and one length after a rectangle will give the area covered by fence

Answer

Given:
- A rectangular field with one side uncovered, leaving a side of 30 feet uncovered.
- The area of the field is 720 sq. feet.

To find:
- The amount of fencing required.

Let's assume the length of the field is L and the width is W.

Area of a rectangle = Length × Width
720 = L × W

Since one side of the field is left uncovered, the field will be fenced on three sides, which means the fencing required will be the perimeter of the rectangle minus the uncovered side.

Perimeter of a rectangle = 2 × (Length + Width)
Perimeter of the field = 2 × (L + W)

Since one side of 30 feet is left uncovered, the perimeter will be the sum of the other three sides.

Perimeter of the field = L + W + L
Perimeter of the field = 2L + W

We can rewrite this equation as:
2L + W = Perimeter of the field

Now, we need to solve these two equations simultaneously to find the values of L and W.

From equation 1:
L × W = 720

From equation 2:
2L + W = Perimeter of the field

Solving these equations simultaneously will give us the values of L and W.

Once we have the values of L and W, we can calculate the perimeter of the field using the equation:
Perimeter of the field = 2L + W

Finally, we will subtract the uncovered side of 30 feet from the perimeter to find the amount of fencing required.

Therefore, the correct answer is option B) 78 feet.

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