A farmer has 52 meters of fencing to make a rectangular corral. If the width is x, what is the length and area?
length = 26-x
area = x(26-x)
To find the length and area of the rectangular corral, we can use the given information that the farmer has 52 meters of fencing.
Let's start by visualizing the rectangular corral. The fence will go around the perimeter of the corral, which consists of two lengths and two widths. We know that the total length of the fence is 52 meters.
Given that the width of the corral is x, we can say that there are two widths, each with a length of x. So, the total length of the fence contributed by the widths is 2x meters.
Since there are two lengths, each length will have a length of (52 - 2x)/2 meters. We divide by 2 because there are two sides contributing to the length.
So, the length of the rectangular corral is (52 - 2x)/2 meters.
Now, let's find the area of the corral. The area of a rectangle is given by the formula: Area = length × width.
Substituting the values we found, the area of the corral is:
Area = [(52 - 2x)/2] × x
= (52x - 2x^2)/2
= 26x - x^2 square meters.
Therefore, the length of the corral is (52 - 2x)/2 meters, and the area of the corral is 26x - x^2 square meters.