IMC 2012 Q20
20. A rectangle with area 125 cm2 has sides in the ratio 4:5. What is the perimeter of the rectangle?
- A 18 cm
- B 22.5 cm
- C 36 cm
- D 45 cm
- E 54 cm
Intermediate Mathematical Challenge 2012, Question 20. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 45 cm
Let the sides of the rectangle, in cm, be \(4x\) and \(5x\).
Then the area of the square is \(4x \times 5x\) cm2 = \(20x^2\) cm2. So \(20x^2 = 125\), that is \(x^2 = \tfrac{25}{4}\).
Therefore \(x = \pm\tfrac{5}{2}\), but \(x\) cannot be negative so \(x = \tfrac{5}{2}\) and so the sides of the rectangle are 10 cm and 12.5 cm. Hence the rectangle has perimeter 45 cm.
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).