Thinking Inside the Box

Geometry Level 2

$R$ is a vertex of the face of a cube whose edges measure 2cm, while $Q$ is the center of the opposite face. Determine the length of $RQ$ .

2.50\text{ cm}

2.25\text{ cm}

\sqrt{5}\text{ cm}

1.25\text{ cm}

\sqrt{6} \text{ cm}

4 solutions

Achille 'Gilles'
Oct 18, 2015

A very clear and accurate answer! Steps are shown beautifully

Abdul Kazi - 5 years, 7 months ago

Thanks! My goal is to give an "elegant" answer.

Achille 'Gilles' - 5 years, 7 months ago

Abdul Kazi
Oct 8, 2015

We can solve this using Pythagorean Theorem Get length of QP by solving for the diagonal line and dividing by 2,

=> root{(2^2)+(2^2)}= root(8), QP= (root(8))/2

Now solve for QR using Pythagorean:

=> [{(root(8)/2)}^2] + 2^2 = root(6).

Alternate: drop perpendicular from Q to line below at point M, the midpoint. MP = 1, RP = 2 so RM = sqrt(2^2 + 1^2) = sqrt(5). RMQ is right triangle, so RQ =sqrt(sqrt(5)^2 + 1^2) = sqrt(6).

Roger Erisman - 5 years, 8 months ago

Nirupam Choudhury
Oct 11, 2015

It would be easier if we keep the box digonal intersection point downwards then by Pythagoras theorem QR=root6

Alan Yan
Oct 10, 2015

Use coordinates! Let $R = (0,0,0)$ and $P = (2, 1, 1)$ . Distance formula implies that the answer is $\sqrt{6}$ .

Wow!!! I should have thought of that.

Debmeet Banerjee - 5 years, 7 months ago

Thinking Inside the Box

4 solutions

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