Farmer Brown has 700 yards of fencing with which to build a rectangular corral divided into two pens. He builds a corral that uses the river as one side so he only has to fence the other 3 sides and the divider down the middle
90
To find the dimensions of the rectangular corral, we need to consider that the total length of fencing used will be the sum of the lengths of the three sides and the divider down the middle.
Let's assume the length of the corral along the river is "x" yards. Since we need to build two pens, we will have two equal lengths across the width of the corral. Let's call this width "y" yards.
So, the lengths of the three sides and the divider down the middle can be represented as follows:
- Length along the river = x yards
- Length across one width = y yards
- Length across the other width = y yards
- Length of the divider = x yards
To calculate the total length of fencing used, we add these four lengths together:
Total length of fencing = x + y + y + x = 2x + 2y
According to the problem, the farmer has 700 yards of fencing. Therefore, we can write the equation:
2x + 2y = 700
Now, we need to solve this equation to find the values of x and y, which will represent the dimensions of the rectangular corral.
Since the equation has two variables, we need another equation to solve the system of equations. But the problem doesn't provide any other information, so we have an indeterminate system. We can use substitution or elimination methods to find possible values.
Let's assume a value for one of the variables, say, x = 200 yards. We can substitute this value into the equation:
2x + 2y = 700
2(200) + 2y = 700
400 + 2y = 700
2y = 700 - 400
2y = 300
y = 300/2
y = 150 yards
So, if x = 200 yards, then y = 150 yards. This means the dimensions of one pen in the corral are 200 yards by 150 yards.
Alternatively, we could assume a different value for x and repeat the substitution process until a suitable solution is found.
It's important to note that there may be multiple valid dimensions for the corral. Therefore, you can try different assumptions for x and find corresponding values for y until you satisfy the condition of having 700 yards of fencing in total.