GK 2018 Q6
6. The large rectangle shown is made up of nine identical rectangles whose longest sides are 10 cm long. What is the perimeter of the large rectangle?
- A 40 cm
- B 48 cm
- C 76 cm
- D 81 cm
- E 90 cm
Grey Kangaroo 2018, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 76 cm
Since the horizontal lengths of the small rectangles are 10 cm, the length of the large rectangle is 2 × 10 cm = 20 cm. Also, since the sum of the heights of five small rectangles is equal to the length of the large rectangle, the height of a small rectangle is 20 cm ÷ 5 = 4 cm. Therefore, the perimeter of the large rectangle is (2 × 20 + 2 × 10 + 4 × 4) cm = 76 cm.
Solution © UK Mathematics Trust, from the GK 2018 solutions.