A Math Forum Project

Current Problem of the Week June 17-21, 1996 A 6 inch by 8 inch piece of paper is folded so that opposite vertices touch. How long is the fold? From these pictures,we can make 2 formulas to help find the length of a and b. a+b = 24    b squared + 18squared = a squared. The 2nd rule comes from the Pythagorean theorem.(a squared + b squared = h squared). It may be changed: b squared + 18 squared = a squared a squared - b squared = 18 squared a squared - b squared = 324 From these 2 rules, I used the guess, check and improve method to find that a=18.75  and  b=5.25 The Pythagorean theorem is then used again: 18 squared + 13.5 squared = fold squared 324+182.25 = fold squared 506.25 = fold squared the square root of 506.25 = fold fold = 22.5cm Changed back to inches, that is 7.5". Steven Brown South Fremantle Senior High School Year 8