A paper has the precise shape of a triangle which is denoted by ABC, with AB = BC = CA = x (say) and, D is a point on BC.
Vertex A is joined onto D forming the crease EF - where E is on AB and F is on AC.
Given that DF is perpendicular to BC, determine:
- The length of EF in terms of x.
- The area of each of the triangles BED, DEF and DFC in terms of x.
The Triangle ABC let AF=h, AE=i, CD=j then
h =root3 / ( 2+root3 )x = (0.4641016x)
i = ( 1.5 + 0.5root3 )/(2+root3 ) x = (0.6339746x)
j = 1/ ( 2+root3 ) x = (0.2679492x)
If perpendicular from D to EF meets EF at G let DG= k & FG=l then
k = ( 1.5 + 0.5root3 )/(2+root3 ) /root2 x = (0.4482877x)
l = root3 /( 2+ root3 )*(root6-root2 )/4 x = (0.1201183x)
Area of BED, DEF & DFC are
1/2*(x-i)*i , 1/2*k*(l+k), 1/2*h*j respectively
Or 0.1160254x2, 0.1274047x2, 0.0621778x2 respectivelyAnd length EF = l+k = 0.568406x
Edited on April 22, 2013, 2:40 am
Posted by Salil
on 2013-04-22 02:25:27