Lesson: Intermediate Problem Solving - 25t05

Practice: Using A Sketch

[Page 25 of 27]

 

Answer each question that follows. Draw a diagram or sketch if you feel that it would help your answer to be more accurate or quicker. Click Continue after you've selected your answer.

1. Routes X, Y, and Z intersect to form a triangle. If route X and route Y intersect at a 20 degree angle and if Z is perpendicular to route X, at what angle do streets Z and Y intersect?
  50 degrees 60 degrees 70 degrees
2. A length of string is knotted at and intervals. If the string is laid flat and horizontal, approximately what fraction of the string's length lies between the sixth and seventh knots from the left?
 
3. A circle with radius 4 is intersected by a single line at points X and Y. The maximum possible distance between X and Y is
  8 4 4


This problem may sound difficult at first since it deals with two figures (a circle and an intersecting line) and asks for a maximum value. However, it's really testing a single geometric concept — the greatest distance between two points on a circle is equal to the diameter, or twice the radius. This is suggested by the key phrase "maximum possible distance".

If you realized at once that you were looking for the diameter you probably didn't bother with a sketch, since the diameter is just twice the radius of 4. But, if you didn't, drawing a quick diagram like this:

would help you to visualize that the maximum distance would be the circle's diameter, which would then lead you to the correct answer of 8:

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