I also have been having some trouble with this problem. How do I set it up?
A rectangular garden is designed so that its length is twice its width. The number of feet in the perimeter of the garden is equal to the number of square feet in its area. What are the dimensions of the garden?
make a sketch and label the width x, then the length must be 2x
the perimeter would be 2(x+2x) = 6x
and the area would be x(2x) = 2x^2
<<The number of feet in the perimeter of the garden is equal to the number of square feet in its area>>
6x = 2x^2
2x^2 - 6x=0
2x(x-3)=0
so x=0, not very likely or
x = 3
so the width is 3 and the length is 6
check: perimeter = 2(3+6) = 18
area = (36) = 18
ok then!
thank you so much!!
To solve this problem, we need to set up equations based on the given information and then solve them to find the dimensions of the garden.
Let's say the width of the garden is "x" feet. According to the problem, the length is twice the width, so the length would be "2x" feet.
The perimeter of a rectangle is found by adding up the lengths of all its sides. In this case, it would be:
Perimeter = 2(length + width)
Since the given information says that the perimeter is equal to the area of the garden, we can set up the following equation:
2(2x + x) = 2x * x
Simplifying this equation, we get:
6x = 2x^2
Now, let's rearrange the equation to bring all terms to one side:
2x^2 - 6x = 0
Next, let's factor out a common factor of 2x:
2x(x - 3) = 0
This equation is satisfied when either 2x = 0 or x - 3 = 0. Since we are dealing with the dimensions of the garden, the value of x cannot be zero. So, we ignore 2x = 0. We focus on the other factor, x - 3 = 0.
Solving x - 3 = 0, we get:
x = 3
Therefore, the width of the garden is 3 feet, and the length is 2 times the width, which is 2(3) = 6 feet.
So, the dimensions of the garden are 3 feet by 6 feet.