web2.0calc
 
+0  
 

 help

0
689
1
avatar

A piece of paper in the shape of an equilateral ABC has AB = 8.  When A is folded over to any point on BC, a crease of length x is formed which joins some point of AC to some point of AB.  As A is moved along BC from B to C, x varies.  If the greatest value of x is M and the least value of x is m, find the ordered pair (M,m).

 Dec 6, 2019

1+0 Answers

 #1
avatar+33615 
+4

The longest crease will occur when A is folded onto B (or C), which gives a crease of length \(M=4\sqrt3\)

 

From the symmetry of the triangle the shortest crease will occur when A is centred between B and C, giving \(m=4\)

 Dec 6, 2019
edited by Alan  Dec 6, 2019

8 Online Users

avatar
avatar
avatar
avatar
avatar
avatar

Top Users

avatar+128474 CPhill moderator
avatar+118609 Melody moderator
avatar+33615 Alan moderator
avatar+14913 asinus moderator
avatar+9519 MaxWong
avatar+3144 admin administrator
avatar+2440 GingerAle
avatar+1791 tomtom
avatar+1484 bader
avatar+1085 parmen
avatar+1032 kittykat

Sticky Topics