Problem: Side AC of right triangle ABC is divided into 8 equal parts. Seven line segments parallel to BC are drawn to AB from the points of division. If BC=10, then the sum of the lengths of the seven line segments:
Answer Choices:
A. can not be found from the given information
B. is 33
C. is 34
D. is 35
E. is 45
Solution:
All the triangles so formed with A as one vertex are similar. Let hk​ be the side parallel to BC at a distance (k/8)⋅AC from A,k=1,2,⋯,7.
​∴(k/8)⋅AChk​​=AC10​;∴hk​=810k​S=h1​+h2​+…+h7​=(810​)(1+2+…+7)=35​
