The area of a rectangle is 15x^2-4x-8 and the width is 5x+2. Which expression best describes the rectangle’s length ? I just need help how to set it up
factor the area, which is width * length
15x^2-4x-8 = (5x+2)(3x-4)
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To find the length of the rectangle, you need to use the formula for the area of a rectangle, which is given by:
Area = Length x Width
In this case, the given area is 15x^2 - 4x - 8, and the width is 5x + 2. Let's set up the equation by replacing the variables accordingly:
(15x^2 - 4x - 8) = Length x (5x + 2)
To solve for the length, we need to isolate it on one side of the equation. Start by distributing the length across the binomial on the right side:
15x^2 - 4x - 8 = 5x * Length + 2 * Length
Now, rearrange the equation in standard form:
15x^2 - 4x - 8 = (5x * Length) + (2 * Length)
Next, combine like terms by moving all the terms to one side of the equation:
15x^2 - 4x - 8 - (5x * Length) - (2 * Length) = 0
Now, we have a quadratic equation in terms of Length. Set the equation equal to zero:
15x^2 - 4x - 8 - (5x * Length) - (2 * Length) = 0
This expression describes the equation for the rectangle's length.