A rectangular garden is fenced on three sides with a wall forming the fourth side. the total length of the fence is 70m. the area if the garden is 600m^2. find the dimensions of the garden.
1. A rectangular pen will be built using 100 feet of fencing. What dimensions will maximize the area?
LW = 600 (1)
L + 2W = 70 or W = (70 - L)/2 (2)
Substitute 2 into 1 and solve for two possible answers.
Which length and width are possible dimensions for the garden
To find the dimensions of the garden, we need to set up a system of equations based on the given information.
Let's assume the length of the rectangular garden is L and the width is W.
According to the problem, the total length of the fence is 70m. Since there are three sides fenced, the total length of the three sides would be 2L + W.
Therefore, our first equation is:
2L + W = 70 ---(Equation 1)
The second piece of information given is the area of the garden, which is 600m^2.
The area of a rectangle is given by the formula A = L x W.
So, our second equation is:
L x W = 600 ---(Equation 2)
To find the dimensions of the garden, we can solve this system of equations.
We can rearrange Equation 1 to solve for W:
W = 70 - 2L
Now, substitute this value of W into Equation 2:
L x (70 - 2L) = 600
Expanding this equation, we get:
70L - 2L^2 = 600
Rearranging, we have:
2L^2 - 70L + 600 = 0
Now, we can solve this quadratic equation. Factoring or using the quadratic formula can give us the values of L.
Once we find the value of L, we can substitute it back into Equation 1 to find the width (W).
Let's solve the quadratic equation:
2L^2 - 70L + 600 = 0
Factoring this equation:
(L - 20)(2L - 30) = 0
From this equation, we get two possible solutions:
L - 20 = 0
L = 20
2L - 30 = 0
L = 15
Now that we have two possible values for L, let's substitute them back into Equation 1 to find the corresponding values of W.
For L = 20:
2(20) + W = 70
40 + W = 70
W = 70 - 40
W = 30
For L = 15:
2(15) + W = 70
30 + W = 70
W = 70 - 30
W = 40
Therefore, the dimensions of the garden can be either:
Length (L) = 20m and Width (W) = 30m
OR
Length (L) = 15m and Width (W) = 40m