GK 2015 Q14
14. Rachel added the lengths of three sides of a rectangle and got 44 cm. Heather added the lengths of three sides of the same rectangle and got 40 cm. What is the perimeter of the rectangle?
- A 42 cm
- B 56 cm
- C 64 cm
- D 84 cm
- E 112 cm
Grey Kangaroo 2015, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 56 cm
Let the length of the rectangle be \(x\) cm and let the width be \(y\) cm. The information in the question tells us that \(2x + y = 44\) and \(x + 2y = 40\). Add these two equations to obtain \(3x + 3y = 84\). Hence \(x + y = 28\) and so the perimeter, which is equal to \(2(x + y)\) cm, is 56 cm.
Solution © UK Mathematics Trust, from the GK 2015 solutions.