### Instruction: A rectangular garden 50 feet long and 10 feet wide is enclosed by a fence. To make the garden larger, while using the same fence, its shape is changed to a square. By how many square feet does this enlarge the garden?### Response: I need to find the difference between the area of the rectangular garden and the area of the square garden, both of which are enclosed by the same fence.
To do that, I need to know the length of the fence, which is the perimeter of the rectangle.
The perimeter of a rectangle is given by the formula 2(length + width), so in this case, the perimeter is 2(50 + 10) = 2(60) = 120 feet.
This means that the square garden also has a perimeter of 120 feet, and the length of each side of the square is 120/4 = 30 feet.
The area of a square is given by the formula side^2, so the area of the square garden is 30^2 = 900 square feet.
The area of the rectangular garden is given by the formula length x width, so the area of the rectangular garden is 50 x 10 = 500 square feet.
Therefore, the difference between the areas is 900 - 500 = 400 square feet.