In rectangle $ABCD$, diagonal $AC = 13$ cm and side $AB = 12$ cm. Side $BC$ is:

In rectangle $ABCD$, diagonal $AC = 13$ cm and side $AB = 12$ cm. Side $BC$ is:
  1. $1$ cm
  2. $5$ cm
  3. $7$ cm
  4. $\sqrt{313}$ cm

Solution

By Pythagoras in right triangle $ABC$: $BC = \sqrt{AC^{2}-AB^{2}} = \sqrt{169-144} = \sqrt{25} = 5$ cm.

Asked in: IMO

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