Question

A rectangular prism must have a base with an area of no more than 27 square meters. The width 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

Answer:

The maximum height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

$A=L*W$

$A\leq 27\ m^{2}$

so

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$-------> using a graphing tool to solve the inequality

The solution for x is the interval---------->$[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

so

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

Answer 2

Its the width
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