Joe plants a rectangular garden in the corner of his field. the area of the garden is 60% of the area of the field. what is the longest side length of Joe's field, in feet. Garden: 16ft x 12ft, Field: 2x ft by 2x ft.
Ag = 16 * 12=192 Ft^2.=Area of garden.
0.6L = 16.
L = 16 / 0.6 = 26.6666 Ft. = Length of longest side.
Correction:
Ag = 16 * 12 = 192 Ft^2.
0.6L = 12.
L = 12 / 0.6 = 20 Ft = Length of longest side.
Af = 20 * 16 = 320 Ft^2.
CHECK: Ag/Af = 192 / 320 = 0.6 = 60%.
To find the longest side length of Joe's field, we need to determine the dimensions of the field based on the given information.
Let's represent the width of the field as '2x' feet, and the length as '2x' feet. Therefore, the area of the field can be calculated as:
Area of field = length * width
Area of field = (2x) * (2x) = 4x^2 square feet
According to the problem, the area of the garden is 60% of the area of the field. Let's calculate the area of the garden:
Area of garden = (16 ft) * (12 ft) = 192 square feet
Since the garden's area is 60% of the field's area, we can set up the following equation:
Area of garden = 0.6 * Area of field
192 square feet = 0.6 * 4x^2 square feet
Solving this equation for x, we get:
4x^2 = (192 square feet) / 0.6
4x^2 = 320 square feet
x^2 = (320 square feet) / 4
x^2 = 80 square feet
x = sqrt(80) feet
x ≈ 8.94 feet
Therefore, the longest side length of Joe's field is approximately 2x = 2 * 8.94 = 17.88 feet.
To find the longest side length of Joe's field, we first need to determine the size of the garden in relation to the field. The problem states that the area of the garden is 60% of the area of the field.
Let's calculate the area of the garden: Length x Width = 16ft x 12ft = 192 square feet.
Since the area of the garden is 60% of the field's area, we can express this mathematically as:
0.6 x Field's Area = Garden's Area
We can further simplify this equation by expressing the field's area in terms of the longest side length, which is denoted as 2x:
0.6 x (2x)^2 = 192
Now we can solve the equation to find the value of x.
First, square the value of 2x:
0.6 x 4x^2 = 192
Next, divide both sides of the equation by 0.6:
4x^2 = 192 / 0.6
Simplifying further:
4x^2 = 320
Divide both sides by 4:
x^2 = 320 / 4
x^2 = 80
Now, take the square root of both sides to solve for x:
√(x^2) = √80
x ≈ 8.94
Since we're interested in the longest side length of the field, we need to multiply x by 2:
Longest side length = 2 x ≈ 2 x 8.94 = 17.88 feet
Therefore, the longest side length of Joe's field is approximately 17.88 feet.