A rectangular plot of land has a fence along three of its four sides. The undenced side and the side opposite the unfenced side have a length that is three times thel length of the other two sides. If the area of the plot is 432 square feet, what is the total length id the fence in feet.
Let's denote the length of the two shorter sides of the rectangular plot as "x" feet each, and the length of the longer sides as "3x" feet each.
The area of a rectangle is given by the formula: Area = Length x Width.
Given that the area of the plot is 432 square feet, we can write the equation:
Area = x * 3x = 3x^2.
Now, we have the equation:
3x^2 = 432.
To find the value of "x," divide both sides of the equation by 3:
x^2 = 432 / 3 x^2 = 144.
Now, take the square root of both sides to solve for "x":
x = √144 x = 12.
So, the length of the shorter sides is 12 feet, and the length of the longer sides is 3x = 3 * 12 = 36 feet.
Now, let's calculate the total length of the fence:
Two shorter sides: 2 * x = 2 * 12 = 24 feet. One longer side: 36 feet.
Total length of the fence = 24 feet + 36 feet = 60 feet.
So, the total length of the fence is 60 feet.
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