if a gardener fences in the total rectangular area shown in the illustration instead of just the square area,he will need twice as much fencing to enclose the garden.how much fencing will he need ?
What illustration?
Well, it seems like the gardener is really thinking outside the box, or in this case, outside the square! If he decides to fence in the entire rectangular area instead of just the square area, he's going to double his fencing needs. So, if he originally needed X amount of fencing for the square area, he will now need 2X to fence in the entire rectangular area. That's twice the fun, I mean, fencing!
To find out how much fencing will be needed to enclose the total rectangular area, we can calculate the perimeter of the rectangle.
Since the area shown in the illustration is a square, each side of the square will be x units.
The perimeter of the square is given by the formula: P = 4s, where s is the side length of the square.
Therefore, the perimeter of the square area is: P1 = 4x.
If the gardener fences in the total rectangular area instead of just the square area, the length and width of the rectangle will be different. Let's assume the length is L units and the width is W units.
The perimeter of the rectangular area is given by the formula: P = 2L + 2W.
According to the given statement, the gardener will need twice as much fencing for the rectangular area compared to the square area. Mathematically, this can be expressed as:
2P1 = P
Substituting the values, we get:
2 * 4x = 2L + 2W
Simplifying this equation, we have:
8x = 2L + 2W
Dividing both sides by 2, we get:
4x = L + W
Therefore, the perimeter of the rectangular area is 4x units.
To find the amount of fencing the gardener will need, we need to compare the lengths of the fence required for both scenarios: enclosing just the square area and enclosing the total rectangular area.
Let's assume the length of one side of the square area is "x". In this case, the gardener would need to fence all four sides, totaling 4x.
Now, if the gardener wants to enclose the total rectangular area shown in the illustration, we need to determine the length and width of the rectangle. Since the square area has a side length of "x" and there is an additional rectangular strip on each side, the total width of the rectangular area becomes x + 2x + x = 4x. The length remains "x".
To calculate the amount of fencing needed to enclose the entire rectangular area, we add up all four sides: 2(length + width) = 2(x + 4x) = 10x.
Thus, the gardener will need ten times more fencing to enclose the total rectangular area compared to just the square area.