PK 2019 Q12
12. The flag of Kangaria is a rectangle with side-lengths in the ratio 3 : 5. The flag is divided into four rectangles of equal area as shown. What is the ratio of the length of the shorter sides of the white rectangle to the length of its longer sides?
- A 1 : 3
- B 1 : 4
- C 2 : 7
- D 3 : 10
- E 4 : 15
Pink Kangaroo 2019, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 4 : 15
Let the length of the white rectangle be \(x\) and its height \(y\). Then the height of the flag is \(3y\) and hence its width is \(5y\). The four rectangles which make up the flag are equal in area, so we have \(3y \times 5y = 4xy\). This simplifies to \(15y = 4x\) (since \(y\) is non-zero) and hence \(y : x = 4 : 15\).
Solution © UK Mathematics Trust, from the PK 2019 solutions.