1957 AHSME Problems/Problem 35

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:

$\textbf{(A)}\ \text{cannot be found from the given information} \qquad \textbf{(B)}\ \text{is }{33}\qquad \textbf{(C)}\ \text{is }{34}\qquad\textbf{(D)}\ \text{is }{35}\qquad\textbf{(E)}\ \text{is }{45}$

Solution

$[asy] import geometry; point B = (0,0); point A = (0,16); point C = (10,0); // Triangle ABC draw(triangle(A,B,C)); dot(A); label("A",A,NW); dot(B); label("B",B,SW); dot(C); label("C",C,SE); // Parallel Lines for (real x=0; x<length(segment(A,B)); x += length(segment(A,B))/8) { pair[] y = intersectionpoints(parallel((0,x),line(B,C)),A--C); draw((0,x)--y[0]); } // Length Label label("$10$", B/2+C/2, S); [/asy]$

$\boxed{\textbf{(D)} \text{ is } 35}$ .

1957 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 34	Followed by Problem 36
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Page

Toolbox

Search

1957 AHSME Problems/Problem 35

Problem

Solution

See Also