A 40-foot by 10-foot rectangular garden is enclosed by a fence. To make the garden larger, while using the same amount of fencing, its shape is changed to a square. How many square feet larger than the old garden is the new garden?
old area = 400 ft^2
perimeter = 20+80 = 100
so
4 s = 100
s = 25
s^2 = area = 625
625 - 400 = ???
Well, let's see here. If we have a 40-foot by 10-foot rectangular garden, the perimeter would be 2(40 + 10), which is 100 feet.
Now, if we want to make the garden into a square while using the same amount of fencing, we have to figure out the new side length of the square. Since all sides of a square are equal, the perimeter of the square would also be 100 feet.
So, to find the side length of the square, we divide the perimeter (100 feet) by 4, and we find that each side of the square would be 25 feet long.
Now, to find the area of the new square garden, we simply multiply the side length (25 feet) by itself, giving us 625 square feet.
To figure out how many square feet larger the new garden is than the old garden, we subtract the area of the old garden (40 feet by 10 feet, which is 400 square feet) from the area of the new garden (625 square feet).
625 - 400 equals 225.
So, the new garden is 225 square feet larger than the old garden. Phew, that was a long journey for a square, wasn't it?
To solve this problem, we need to find the area of both the old rectangular garden and the new square garden.
First, let's find the area of the old rectangular garden. The formula to calculate the area of a rectangle is length times width. In this case, the length is 40 feet and the width is 10 feet. So, the area of the old garden is 40 feet * 10 feet = 400 square feet.
Now, let's find the area of the new square garden. Since the square has equal sides, we just need to find the length of one side.
To do this, we need to calculate the perimeter of the old rectangular garden, which is equal to the amount of fencing used. The formula for the perimeter of a rectangle is 2 times the sum of length and width.
The perimeter of the old garden is 2 * (40 feet + 10 feet) = 100 feet.
Since we need to use the same amount of fencing for the new garden, the perimeter of the square garden will also be 100 feet.
The formula to calculate the side length of a square, given the perimeter, is perimeter divided by 4. So, the side length of the square garden is 100 feet / 4 = 25 feet.
Now, let's calculate the area of the square garden. The formula for the area of a square is side length times side length. So, the area of the square garden is 25 feet * 25 feet = 625 square feet.
To find out how many square feet larger the new garden is compared to the old garden, we subtract the old garden's area from the new garden's area.
625 square feet (area of the new garden) - 400 square feet (area of the old garden) = 225 square feet.
Therefore, the new garden is 225 square feet larger than the old garden.
40 * 10 = 400 square feet
The fence is 100 feet long
25 * 25 = 625 square feet