IMC 2006 Q14
14. A 3 × 8 rectangle is cut into two pieces along the dotted line shown. The two pieces are then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?
- A 21
- B 22
- C 23
- D 24
- E 25
Intermediate Mathematical Challenge 2006, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 24
The diagram shows that the two pieces will fit together to form a right-angled triangle which has base 8 and height 6. The length of the hypotenuse = \(\sqrt{6^2 + 8^2}\), that is 10, so the perimeter of the triangle is 24.
Solution © UK Mathematics Trust, from the IMC 2006 solutions.