1954 AHSME Problems/Problem 45

In a rhombus, $ABCD$ , line segments are drawn within the rhombus, parallel to diagonal $BD$ , and terminated in the sides of the rhombus. A graph is drawn showing the length of a segment as a function of its distance from vertex $A$ . The graph is:

$\textbf{(A)}\ \text{A straight line passing through the origin.}\\ \textbf{(B)}\ \text{A straight line cutting across the upper right quadrant.}\\ \textbf{(C)}\ \text{Two line segments forming an upright V.}\\ \textbf{(D)}\ \text{Two line segments forming an inverted V.}\\ \textbf{(E)}\ \text{None of these.}$

Solution

Note that the length of the segment increases linearly with distance from $A$ , starting at zero, until it passes side $BD$ (this can be shown with similar triangles). From there, it decreases linearly until it reaches zero at point $C$ (this can also be shown with similar triangles). The only shape that matches this description is that of choice $\boxed{\textbf{(D)}}$ , so that is our answer and we are done.

1954 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 44	Followed by Problem 46
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1954 AHSME Problems/Problem 45

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