I REALLY need help on math because I can't understand what my teacher is saying in class.
Here's the question : Sixteen metres of fencing are available to enclose a rectangular garden.
a) represent the area of the garden as a function of the legnth of one side.
b) graph the function
c) what dimensions provide an area greater than 12 m ^2?
Please help me learn how to do this.
I'd appreciate it! =D
Assistance needed.
Please type your subject in the School Subject box. Any other words are likely to delay responses from a teacher who knows that subject well.
the the width be x
then the width is 8-x
a) Area = x(8-x)
b) graph it
c)
w l Area
1 7 7
2 6 12
3 5 15
4 4 16
5 3 15
6 2 12
7 1 7
mmmmhhh?
Of course! I'd be happy to help you with this math problem step by step.
a) To represent the area of the garden as a function of the length of one side, let's start by understanding the given information.
We know that the garden is rectangular, which means it has two pairs of equal sides. Let's assume one side of the rectangle has a length "x" meters. Since there are four sides in a rectangle, the other side will also have a length of "x" meters.
Now, let's calculate the perimeter of the garden using the given information that 16 meters of fencing are available. The perimeter is the sum of all four sides, so it would be: 2x + 2x = 4x.
Since the perimeter is 16 meters, we have the equation: 4x = 16.
To find the solution for "x," divide both sides of the equation by 4:
4x/4 = 16/4,
x = 4.
Now, we know that one side of the rectangle has a length of 4 meters. To represent the area of the garden as a function of the length of one side, we use the formula for the area of a rectangle, which is length multiplied by width. So, the area is given by: A = x * x = x^2.
In this case, since we know that one side length is 4 meters, the area of the garden as a function of one side length (x) is: A(x) = 4^2 = 16 square meters.
b) To graph the function A(x) = 16, we can set up a coordinate plane and plot a point on the graph. The x-axis represents the length of one side of the rectangle, and the y-axis represents the area. Since A is always 16, the graph will be a horizontal line passing through the y-axis at 16.
c) To find the dimensions that provide an area greater than 12 square meters, we need to solve the inequality A(x) > 12.
Substituting the function A(x) = x^2, we have:
x^2 > 12.
To solve this inequality, we can take the square root of both sides:
√(x^2) > √12, or
|x| > √12.
Since we are dealing with positive values for side length, we can rewrite this as:
x > √12 or x < -√12.
However, since side lengths cannot be negative in this context, we can disregard the x < -√12 solution.
The dimensions that provide an area greater than 12 square meters are x > √12.
I hope this helps you understand how to approach and solve this math problem. Let me know if you have any further questions!