Arectangular 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=

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

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: