PK 2020 Q15
15. A vertical stained glass square window of area 81 cm2 is made out of six triangles of equal area (see figure). A fly is sitting on the exact spot where the six triangles meet. How far from the bottom of the window is the fly sitting?
- A 3 cm
- B 5 cm
- C 5.5 cm
- D 6 cm
- E 7.5 cm
Pink Kangaroo 2020, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 6 cm
Let \(h\) be the height of the fly above the base of the window. Each side-length of the square window of area 81 cm2 is 9 cm. The two triangles that form the bottom part of the window have total area equal to a third of the whole window, namely 27 cm2. Hence \(\tfrac{1}{2} \times 9 \times h = 27\) so \(h = 27 \times 2 \div 9 = 6\) cm.
Solution © UK Mathematics Trust, from the PK 2020 solutions.