Answer:
See answers below.
Step-by-step explanation:
Large Rectangle: length x width = (x + 3)(x - 4) =
x² - 4x + 3x - 12
x² - x - 12
Smaller Rectangle: length x width = (x)(3) = 3x
Shaded Region: shaded area = lg. rectangle minus small rectangle
A = (x² - x - 12) - 3x
A = x² - 4x - 12
Solve for x, if shaded reion's area is 48 square units:
48 = x² - 4x - 12
x² - 4x - 12 -48 = 0
x² - 4x - 60 = 0
(x - 10)(x + 6) = 0
x - 10 = 0 or x + 6 = 0
x = 10 or x = -6
But x represents a length, so x cannot be -6.
x = 10
