The area of Mrs.Raders rectangular garden is 100 square feet. One side is a stone wall. She encloses the other 3 sides with 30 feet of fencing. What are the dimensions of her garden?
I have the length of the triangle to be 30-2x and the width to be x.
But soo how would you put that equation together?
Would it be x(32-2x)=100...cuz i cant get it to come out right.
PLEASE HELP!
It is not a triangle. The stone wall is one side of a rectangle, and the fence is the other three sides of the rectangle.
30=2L + W
LW=100
solve for
W in the first equation, put that for w in the second. Notice you get a quadratic equation, solve it.
To solve this problem, let's break it down step by step:
1. Let's start by assigning variables for the dimensions of the garden. Let L be the length of the garden and W be the width of the garden.
2. From the given information, we know that one side of the garden is a stone wall, which means it doesn't require fencing. Therefore, the perimeter of the garden is the sum of the remaining three sides: 2L + W.
3. We are also given that the perimeter of the garden with fencing is 30 feet. So we can write the equation 2L + W = 30.
4. Additionally, we are given that the area of the garden is 100 square feet. The area of a rectangle is calculated by multiplying the length and width, which means LW = 100.
5. Now we have two equations:
2L + W = 30 (equation 1)
LW = 100 (equation 2)
6. To solve for the dimensions of the garden, we need to eliminate one variable. Let's solve equation 1 for W:
W = 30 - 2L
7. Substitute this expression for W in equation 2:
L(30 - 2L) = 100
8. Now we have a quadratic equation that we can solve by expanding and rearranging terms:
30L - 2L^2 = 100
-2L^2 + 30L - 100 = 0
9. Rearrange the equation to standard quadratic form:
2L^2 - 30L + 100 = 0
10. Solve the quadratic equation by factoring or by using the quadratic formula. The solutions for L will give you the lengths of the garden.
11. Once you find the values of L, substitute them back into the equation W = 30 - 2L to find the corresponding widths of the garden.
12. Check that both the length and width values satisfy the conditions of the problem (such as positive values and the given perimeter equation).
By following these steps, you should be able to find the dimensions of Mrs. Rader's garden.