A family decides to grow flowers in their garden. They have 56 feet of fence they want to cut into two pieces to make two square gardens. How long should each piece be if they want the total area of the squares to be 100 square feet?
10
100ft^2/2 = 50 ft^2/sq.
s^2 = 50, s = 7.071 ft.
7.071ft/side * 8sides = 56.57 ft = total required. But we have only 56 ft.
Correction: Ignore the "10".
To find the length of each piece of the fence, we need to determine the perimeter of each square garden, knowing that the total area of both squares is 100 square feet.
1. Let's assume that the length of the first piece of the fence is x feet. The second piece of the fence will then be 56 - x feet.
2. The perimeter of a square garden is equal to four times the length of one side. So, for the first square garden, the perimeter will be 4x feet, and for the second square garden, it will be 4(56 - x) feet.
3. We need to make the total area of both squares equal to 100 square feet. The area of a square garden is given by the formula side^2. For the first square garden, the area will be x^2 square feet, and for the second square garden, it will be (56 - x)^2 square feet.
4. Since the total area is 100 square feet, we have the equation: x^2 + (56 - x)^2 = 100.
5. Expanding and simplifying the equation, we get: x^2 + 3136 - 112x + x^2 = 100.
6. Combining like terms, we have: 2x^2 - 112x + 3036 = 100.
7. Subtracting 100 from both sides of the equation, we get: 2x^2 - 112x + 2936 = 0.
To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, factoring is the most convenient approach.
8. By factoring, we find: (2x - 74)(x - 40) = 0.
Setting each factor equal to zero gives us two solutions: 2x - 74 = 0 and x - 40 = 0.
9. Solving each equation, we get two possible values for x: x = 37 or x = 40.
So, the length of each piece of the fence can be either 37 feet or 40 feet, depending on the configuration of the gardens.