1954 AMC 12 Problem 45
Attempt Problem 45 of the 1954 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1954 AMC 12 solutions, or check the answer key.
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45.
In a rhombus line segments are drawn within the rhombus, parallel to diagonal 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 The graph is:
a straight line passing through the origin.
a straight line cutting across the upper right quadrant.
two line segments forming an upright
two line segments forming an inverted
none of these.
Answer: D
Small hint:
Imagine moving a segment parallel to from toward the opposite vertex
Big hint:
Its length grows linearly to the full diagonal and then decreases linearly to zero
Solution:
Starting at the parallel cross section has length and grows linearly until it reaches the diagonal Continuing toward the opposite vertex, its length decreases linearly back to The graph is therefore made of two line segments forming an inverted
Thus, the correct answer is D.