Answer:
The maximum height is 12 m
Step-by-step explanation:
Area of rectangular prism base:
A = l*w
where l is length and w is width (both in meters)
A ≤ 27
The width of the base must be 9 meters less than the height (h, also in meters):
h - 9 = w
The length of the base must be 6 meters more than the width of the base:
w + 6 = l
Combining with the previous equation:
h - 9 + 6 = l
h - 3 = l
Replacing with the area formula:
(h - 3)*(h - 9) ≤ 27
h² - 9*h - 3*h + 27 ≤ 27
h² - 12*h ≤ 0
One solution is h = 0, the other one is:
h ≤ 12
then, the maximum height is 12 m
