A rectangle has an area represented by the expression x^2-7x-8 = a
The shortest side can be represented as x - k
What is the value of K?
well, x^2-7x-8 factors to
(x-8)(x+1) = 0
So the sides are (x-8) and (x+1)
So what are your thoughts on this?
Good, I get it now
To find the value of k, we need to understand the characteristics of the rectangle in terms of its sides and area.
Given that the area of the rectangle is represented by the expression x^2 - 7x - 8 = a, we can set up the equation:
x^2 - 7x - 8 = a
To find the value of k, we need to determine the shortest side of the rectangle. Let's assume that x - k represents the shortest side.
The area of a rectangle is calculated by multiplying the length and width. In this case, the length is x and the width is x - k.
Now we can set up the equation using the formula for the area of a rectangle:
Length * Width = Area
(x) * (x - k) = a
x(x - k) = a
Expanding the equation, we get:
x^2 - kx = a
Comparing this equation to the given area expression, we have:
x^2 - 7x - 8 = x^2 - kx
We can equate the coefficients of the like terms:
-7x = -kx
To find the value of k, we need to isolate the variable k. Let's divide both sides of the equation by -x:
-7x / -x = -kx / -x
Simplifying, we get:
7 = k
So, the value of k is 7.