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

Question

1 month ago

8

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 =

Mathematics

2 answers:

Leona [12.6K] · Answer 1 · 2026-03-04T22:27:42+03:00

Answer:

The upper limit for the height of the prism is $12\ m$

Step-by-step explanation:

Let

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

It is known that

the area of the base of the prism must not exceed

$A=L*W$

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

thus

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

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

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

Insert equation B into equation C

$L=(x-9)+6$

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

Substituting equations B and D into inequality A

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

The resultant solution for x lies in the interval----------> $[0,12]$

consult the attached figure

but bear in mind that

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

thus

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

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

tester [12.3K] · Answer 2 · 2026-03-04T22:29:47+03:00

tester [12.3K]1 month ago

7 0

The measurement pertaining to the breadth
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