By algebraic approach we find that the compound shape is represented by the equation 2 · x² - 5 · x - 18 = 0 and the length of the line segment AB is 4.5 units.
How to find the total area of a compound shape
The total area of the compound shape is the sum of the areas of the two rectangles, whose entire expression is:
A = x · (x - 4) + 2 · x · (x - 2) (1)
Then, we proceed to expand this expression by algebraic means:
A = x² - 4 · x + 3 · x² - 6 · x
A = 4 · x² - 10 · x
4 · x² - 10 · x - 36 = 0
2 · x² - 5 · x - 18 = 0
We need to solve the quadratic equation to determine the possible values of line segment AB. Please notice that lengths are nonzero positive integers:
2 · x² - 5 · x - 18 = 0
(x - 4.5) · (x + 2) = 0
There is only possibility for the length of the line segment AB: x = 4.5.
To learn more on quadratic functions: https://brainly.com/question/5975436
#SPJ1
