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A surveyor marks a triangular plot with base 12 m and wants the two other sides to differ by exactly 4 m, with the base angle at one end 60°.
Using the difference-of-sides idea, is this plot constructible?

Class 9Constructions of TrianglesGeometry
  • AYes, since 4 m < 12 m
  • BNo, since 4 m < 12 m
  • CYes, since 4 m = 12 m / 3
  • DNo, since the difference must exceed the base

Step-by-Step Solution

For the difference-of-sides construction the difference of the two sides must be less than the base. Here 4 < 12, so the plot can be constructed.
Answer: A) Yes, since 4 m < 12 m

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