Answer :
Final answer:
The correct quadratic equation representing the area of the rectangle is A) x^2 - 6x - 114 = 0, derived from the equation for the area of a rectangle and the given conditions.
Explanation:
The problem here provides the following relationships: the length of a rectangle is 6 meters more than its width and the area of the rectangle is 114 square meters. We are asked to identify the correct quadratic equation representing the area of the rectangle, given x represents the width.
Area of a rectangle is given by length multiplied by the width, or L*W. Here, the length is described as x+6 (because it is 6 meters more than the width), and the width is x. Therefore, the equation representing the area of the rectangle is (x+6)*x.
This can be written as x^2+6x. We also know that the area equals 114, which gives us the equation x^2+6x-114 = 0. Therefore, the correct option is A) x^2 - 6x-114 = 0.
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Answer:
last one
Step-by-step explanation:
x = width
x+6 = length
Area = length times width
x(x + 6) = [tex]x^{2}[/tex] + 6x
[tex]x^{2}[/tex] + 6x = 114 (subtract 114 from both sides)
[tex]x^{2}[/tex] + 6x -114 = 0
