The height, width and length of a small box are consecutive integers with the height being the smallest of the three dimensions. If the length and width are increased by 2 cm each and the height is tripled,
then the volume of the box is increased by 552 cm3
. Use algebraic techniques to find the dimensions of
the original small box.

9514 1404 393

  4 cm, 5 cm, 6 cm

Step-by-step explanation:

If x represents the height of the original box, the other two dimensions are ...

  width = x+1

  length = x+2

and the volume is ...

  V = HWL = x(x +1)(x +2) = x³ +3x² +2x

__

After the change in dimensions, the height is 3x, the width is x+3, and the length is x+4. The new volume is ...

  V = HWL = 3x(x+3)(x+4) = 3x³ +21x² +36x

The difference in volumes is ...

  (3x³ +21x² +36x) -(x³ +3x² +2x) = 552

In standard form, this equation is ...

  2x³ +18x² +34x -552 = 0

Factoring out 2 gives ...

  x³ +9x² +17x -276 = 0

Possible rational roots are 1, 2, 3, 4, 6, and other divisors of 276. The largest possibility worth considering is less than ∛276 ≈ 6.5. Trial and error, or a graphing calculator can show us that x=4 is the only real solution to this equation.

The dimensions of the original small box are 4 cm × 5 cm × 6 cm.

to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

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