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Difference between revisions of "1957 AHSME Problems/Problem 35"

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== Solution ==
 
== Solution ==
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<asy>
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import geometry;
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point B = (0,0);
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point A = (0,16);
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point C = (10,0);
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// Triangle ABC
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draw(triangle(A,B,C));
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dot(A);
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label("A",A,NW);
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dot(B);
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label("B",B,SW);
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dot(C);
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label("C",C,SE);
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// Parallel Lines
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for (real x=0; x<length(segment(A,B)); x += length(segment(A,B))/8) {
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  pair[] y = intersectionpoints(parallel((0,x),line(B,C)),A--C);
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  draw((0,x)--y[0]);
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}
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// Length Label
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label("$10$", B/2+C/2, S);
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</asy>
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<math>\boxed{\textbf{(D)} \text{ is } 35}</math>.
 
<math>\boxed{\textbf{(D)} \text{ is } 35}</math>.
  

Revision as of 07:55, 26 July 2024

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]

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

See Also

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

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