The rectangle on it's smaller right side says x-2 and it's longer bottom side says x+8 if the area of the rectangle is 39 square ft what is the value of x
To find the value of x, we need to set up an equation using the area of a rectangle formula:
Area = length * width
Given that the length is x + 8 and the width is x - 2, we can set up the equation as:
(x + 8)(x - 2) = 39
Expanding the equation:
x^2 + 8x - 2x - 16 = 39
x^2 + 6x - 16 = 39
x^2 + 6x - 55 = 0
Now we need to solve for x by factoring the quadratic equation. The factors of -55 that sum to 6 are 11 and -5:
(x + 11)(x - 5) = 0
Setting each factor to zero gives:
x + 11 = 0 or x - 5 = 0
x = -11 or x = 5
Since the length of the rectangle cannot be negative, the value of x is 5.