Dimensions of a Box A large plywood box has a volume of . Its length is ft greater than its height, and its width is ft less than its height. What are the dimensions of the box

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02-09-2020
Mathematics

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Dimensions of a Box A large plywood box has a volume of . Its length is ft greater than its height, and its width is ft less than its height. What are the dimensions of the box

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AbsorbingMan AbsorbingMan · Answer 1 · 2020-09-02T05:29:46+02:00

Answer:

Few things are missing, they are volume of the box is 180 feet cube. Length is 9 feet greater than its height, and weight is 4 feet less than its height.

Step-by-step explanation:

Given, the volume of the box, V = 180 feet cube

Let the height of the box, h = x feet

Therefore, length is, l = ( 9+x ) feet

And width is, b = ( x-4) feet

so volume of the box is

V = l x b x h

[tex]$ 180= (x+9) \times (x-4) \times (x)$[/tex]

[tex]$ x^3 +5x^2-36x -180 =0$[/tex]

Factorizing we get

(x+5)(x-6)(x+6)=0

Therefore,

x = -5, -6, 6

Now since the height of the box cannot be negative, so taking the positive value of x, we get

Height of the box, h = x = 6 feet

Length , l = ( 9+x ) = 9+6 = 15 feet

Width , b = ( x-4) = 6-4 = 2 feet