IMC 2005 Q18
18. Three-quarters of the area of the rectangle has been shaded.
What is the value of \(x\)?
- A 2
- B 2.4
- C 3
- D 3.6
- E 4
Intermediate Mathematical Challenge 2005, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 4
The area of the rectangle is 48 cm2, so the unshaded area is 12 cm2. Therefore \(\tfrac{1}{2} \times x \times 2 + \tfrac{1}{2} \times (6 - x) \times 8 = 12\), that is \(x + 24 - 4x = 12\), so \(x = 4\).
Solution © UK Mathematics Trust, from the IMC 2005 solutions.