Answer: 10 feet by 8 feet
Step-by-step explanation:
The area of a rectangle is given by the formula:
A = L·W, where:
In this case:
Let's plug these into the formula:
A = L·W
80 = (2W - 6)·(W)
Use the distributive property to multiply the two terms together on the right side:
80 = 2W² - 6W
Now, solve the equation for W. We can solve this quadratic equation by subtracting 80 from both sides to set the equation equal to 0:
2W² - 6W - 80 = 0
Factor the quadratic equation:
2(W² - 3W - 40) = 0
2(W - 8)(W + 5) = 0
Now, we have 2 possible solutions for W:
W = 8 and W = -5. Since width cannot be negative, W = 8 feet.
Now, we can find the length (L) using the expression above:
L = 2W - 6
L = 2(8) - 6
L = 10 feet
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