If the area of a rectangle is 39 square feet, find the value of x; when they give the horizontal as x + 8 and the vertical as x -2
To find the area of the rectangle, we can use the formula:
Area = length x width
Given that the horizontal side is x + 8 and the vertical side is x - 2, we can write the equation for the area as:
(x + 8)(x - 2) = 39
Expanding this equation, we get:
x^2 - 2x + 8x - 16 = 39
x^2 + 6x - 16 = 39
x^2 + 6x - 55 = 0
Now we need to solve this quadratic equation for x. We can either factor it or use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 6, and c = -55. Substituting these values into the formula, we get:
x = (-6 ± √(6^2 - 4(1)(-55))) / 2(1)
x = (-6 ± √(36 + 220)) / 2
x = (-6 ± √256) / 2
x = (-6 ± 16) / 2
This gives us two possible solutions for x:
x = (-6 + 16) / 2 = 10 / 2 = 5
x = (-6 - 16) / 2 = -22 / 2 = -11
Since the length of a side cannot be negative, the only valid solution is x = 5. Therefore, the value of x is 5.