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Answer:

Step-by-step explanation:

Given

Length of the base of the rectangular box [tex]= 2x +5[/tex]

Width  of the base of the rectangular box [tex]= x[/tex]

Area of the base of the rectangular box

[tex]= (2x + 5)(x)\\= 2x^2 + 5x[/tex]

a) Given

Area of the base of the rectangular box [tex]= 58[/tex] square centimeter

It can also be written as

[tex]2x^2 + 5x = 58\\2x^2 + 5x - 58 = 0[/tex]

b) See the attached image

c) Volume

Base Area * height

[tex]58 * (x-2)[/tex]

[tex]x = -1.25 + \frac{22.11}{4} \\x = 4.27[/tex]

Volume [tex]= 58 * 4.27 = 248.09[/tex] cubic centimeter

View image Podgorica
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