Problem:
In the figure shown below, ABCDE is a regular pentagon and AG=1. What is FG+JH+CD?
Answer Choices:
A. 3
B. 12−45
C. 35+25
D. 1+5
E. 1011+115
Solution:
Triangles AGB and CHJ are isosceles and congruent, so AG=HC=HJ=1. Triangles AFG and BGH are congruent, so FG=GH. Triangles AGF,AHJ, and ACD are similar, so ba=ca+b=d2a+b.
Because a=c=1, the first equation becomes b1=11+b or b2+b−1=0, so b=2−1+5. Substituting this in the second equation gives d=21+5, so b+c+d=(D)1+5.
