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Elena L
22 hours 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 [4.1K]22 hours ago
8 1

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 [3.9K]21 hour ago
7 0
The measurement pertaining to the breadth
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