IMC 2015 Q15
15. A flag is in the shape of a right-angled triangle, as shown, with the horizontal and vertical sides being of length 72 cm and 24 cm respectively.
The flag is divided into 6 vertical stripes of equal width.
What, in cm2, is the difference between the areas of any two adjacent stripes?
- A 96
- B 72
- C 48
- D 32
- E 24
Intermediate Mathematical Challenge 2015, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 48
The stripes are of equal width, so the width of each stripe is (72 ÷ 6) cm = 12 cm. The diagram shows that the difference between the areas of any two adjacent stripes is equal to the area of a rectangle of width 12 cm and height \(h\) cm. By similar triangles, \(\dfrac{h}{12} = \dfrac{24}{72}\). So \(h = \dfrac{12 \times 24}{72} = 4\). So the required area is 12 × 4 cm2 = 48 cm2.
Solution © UK Mathematics Trust, from the IMC 2015 solutions. Longer versions with investigations: Solutions and investigations (PDF).