Question

A rectangular prism must have a base with an

area of no more than 27 square meters. The widt!
of the base must be 9 meters less than the height
of the prism. The length of the base must be 6
meters more than the width of the base. Find the
maximum height of the prism.
Let x = the height of the prism
X-9=

Answer 1

13.5

Explanation:

area of base < 27 m^2

width = height - 9

length = 6

area of base = width * length

(height - 9)*6 < 27

height < 27/6 + 9

height < 13 .5 (maximum height)

Answer 2

The maximum height is 12 m

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