a rectangular garden is located adjacent to a house the family needs to fence in the garden the family wants three side because one side is up against the house the length is 5 meters longer than the width and the area of the garden is 204 square meters how much fence is needed
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To determine how much fence is needed, we need to calculate the perimeter of the garden.
Let's assign variables to the information given:
- Let W represent the width of the garden.
- Since the length is 5 meters longer than the width, the length would be W + 5.
The formula for the area of a rectangle is A = length * width.
In this case, the area is given as 204 square meters, so we can create the following equation:
204 = (W + 5) * W
To solve this equation, we can use the quadratic formula, but in this case, we can easily solve it by factoring. Rearranging the equation, we have:
W^2 + 5W - 204 = 0
Let's factor this quadratic equation:
(W + 17)(W - 12) = 0
From here, we have two possible values for W: W = -17 or W = 12. Since width cannot be negative, we discard W = -17.
So, the width of the garden is 12 meters, and the length is 12 + 5 = 17 meters.
To find the perimeter, we use the formula: P = 2 * (length + width).
P = 2 * (17 + 12)
P = 2 * 29
P = 58
Therefore, you would need 58 meters of fence to enclose the garden.