The total area of all the faces of a rectangular solid is 22 cm^2, and the total length of all its edges is 24 cm. Then the length in cm of any one of its internal diagonals is

1984 AMC 12 Problem 25

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25.

The total area of all the faces of a rectangular solid is

22\text{ cm}^2,

and the total length of all its edges is

24\text{ cm}.

Then the length in cm of any one of its internal diagonals is

\sqrt{11}

\sqrt{12}

\sqrt{13}

\sqrt{14}

not uniquely determined

Let the side lengths be

x,y,z

and translate both totals into equations

Expand

(x+y+z)^2

to find

x^2+y^2+z^2

The conditions give

2(xy+xz+yz)=22

and

4(x+y+z)=24,

xy+xz+yz=11

and

x+y+z=6.

Hence the square of an internal diagonal is

x^2+y^2+z^2=6^2-2(11)=14.

Its length is

\sqrt{14}.

Therefore, the correct answer is D.