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UKMT Junior Mathematical Challenge, 2022

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a seven-sided polygon, $PQRSTUV$ . It is formed from two equilateral triangles $PQW$ and $STU$ of side-length 5 cm and 8 cm respectively. The two triangles overlap in an equilateral triangle of side-length 2 cm. What is the perimeter of $PQRSTUV$ ?

(A) $27\text{ cm}$ (B) $30\text{ cm}$ (C) $33\text{ cm}$ (D) $36\text{ cm}$ (E) $39\text{ cm}$

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