A rectangular region with one side against an existing building is to be fenced in. Assume that there is 150 ft of material available. Since one side is the building, you will use your material to construct 3 sides of the rectangle.
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To determine the dimensions of the rectangle, we can set up an equation using the given information.
Let's assume the length of the rectangle is L and the width is W. Since one side of the rectangle is against the existing building, we need to find the perimeter of the remaining three sides.
The perimeter of a rectangle is given by the formula: perimeter = 2L + 2W.
In this case, we will use the available material to construct the three sides, which means the perimeter should be equal to 150 ft.
Therefore, we have the equation: 2L + 2W = 150.
To solve for either length or width, we can rearrange the equation. Let's solve for L:
2L + 2W = 150
2L = 150 - 2W
L = (150 - 2W)/2
L = 75 - W
Now, we can express the width W in terms of L by rearranging the equation:
2L + 2W = 150
2W = 150 - 2L
W = (150 - 2L)/2
W = 75 - L
We now have two equations that describe the relationship between L and W:
L = 75 - W
W = 75 - L
We can find the possible values for L and W by trying different combinations that satisfy both equations.
For example, if we assume L = 30, then W = 75 - 30 = 45.
We can verify if this combination satisfies the perimeter equation:
2L + 2W = 2(30) + 2(45) = 60 + 90 = 150
Therefore, one possible solution is a rectangle with a length of 30 ft and a width of 45 ft.