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MathNet 2012 Question 37

Math Olympiad Vault · MathNet 2012

Question 37

The six triangles in the figure are right triangles, and their angles at $A$ are equal. Also, $AB=24\,\mathrm{cm}$ and $AC=54\,\mathrm{cm}$. What is the length of $AD$?

Question illustration

A) $30\,\mathrm{cm}$; B) $34\,\mathrm{cm}$; C) $36\,\mathrm{cm}$; D) $38\,\mathrm{cm}$; E) $39\,\mathrm{cm}$.