enigma123 wrote:

If the box shown is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C?

A)10%

B)20%

C)30%

D)40%

E)50%

Any idea how to solve this guys?

AC is the edge of the cube. Let's say its length is 'a'.

AB is just the diagonal of a face of the cube i.e. the diagonal of the square whose each side is of length 'a'. Using pythagorean theorem, we know that AB =\(\sqrt{2}a\)

Now think of the two dimensional triangle ABC (it is right angled at A)

AC = a and AB = \(\sqrt{2}a\)

Again using pythagorean theorem, \(BC^2 = a^2 + (\sqrt{2}a)^2\)

\(BC = \sqrt{3}a\)

So, \((BC - AB)/AC * 100 = (\sqrt{3} - \sqrt{2}) * 100 = (1.732 - 1.414) * 100 = apprx 30%\)

By the way, you would probably be given the value of root 3.

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