GK 2016 Q11
11. A 3 cm wide strip is grey on one side and white on the other. Maria folds the strip, so that it fits inside a rectangle of length 27 cm, as shown. The grey trapeziums are identical. What is the length of the original strip?
- A 36 cm
- B 48 cm
- C 54 cm
- D 57 cm
- E 81 cm
Grey Kangaroo 2016, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 57 cm
Let the length of the shorter of the two parallel sides of the grey trapeziums be \(x\) cm. Since the folded shape is 27 cm long and the strip is 3 cm wide, we have \(3 + x + 3 + x + 3 + x + 3 + x + 3 = 27\) which has solution \(x = 3\). Hence the length of the longer of the two parallel sides of the grey trapezium is \((3 + x + 3)\) cm = 9 cm. Also, since the height of each trapezium is equal to the width of the strip, the height is 3 cm and hence the height of each of the small rectangles is (6 − 3) cm. Therefore the total length of the strip (along the edge marked in the diagram) is
Solution © UK Mathematics Trust, from the GK 2016 solutions.