A rectangular garden is fenced on thee sides with a wall forming the fourth side. The total length of the fence is 70m. The area of the garden is 600m^2. Find the dimensions of the garden.
30 * 20
To find the dimensions of the garden, we can set up a system of equations based on the given information.
Let's assume that the length of the garden is L meters and the width of the garden is W meters.
First, we know that the total length of the fence is 70m. Since there are three sides surrounding the garden, each with a length of L or W, we can set up an equation:
2L + W = 70 (Equation 1)
Next, we are given that the area of the garden is 600m^2. The area of a rectangle is found by multiplying the length by the width, so we have another equation:
L * W = 600 (Equation 2)
Now we have a system of two equations with two unknowns. We can solve this system to find the dimensions of the garden.
We can start by solving Equation 1 for W:
W = 70 - 2L
Now substitute this value of W into Equation 2:
L * (70 - 2L) = 600
Expanding and rearranging the equation:
70L - 2L^2 = 600
Rearranging the equation and setting it equal to zero:
2L^2 - 70L + 600 = 0
Now we can solve this quadratic equation. Factoring or using the quadratic formula will give us the values of L. Let's use factoring here:
(2L - 20)(L - 30) = 0
Setting each factor equal to zero:
2L - 20 = 0 --> L = 10
L - 30 = 0 --> L = 30
Now we have two possible values for L. Plugging each value back into Equation 1, we can find the corresponding value for W:
For L = 10:
2(10) + W = 70
20 + W = 70
W = 50
For L = 30:
2(30) + W = 70
60 + W = 70
W = 10
So, we have two sets of dimensions for the garden:
If L = 10 and W = 50, the dimensions are 10m by 50m.
If L = 30 and W = 10, the dimensions are 30m by 10m.
Therefore, the dimensions of the garden can be either 10m by 50m or 30m by 10m.