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A student must construct triangle ABC with base BC = 7 cm, base angle B = 45° and AB + AC = 6 cm.
Why is this construction impossible?

Class 9Constructions of TrianglesGeometry
  • ABecause AB + AC = 6 cm is less than the base BC = 7 cm
  • BBecause angle B is too small
  • CBecause 6 cm is even
  • DBecause the base must be 6 cm

Step-by-Step Solution

The sum of the other two sides must be greater than the base (triangle inequality). Since 6 < 7, no triangle exists, so the construction cannot be done.
Answer: A) Because AB + AC = 6 cm is less than the base BC = 7 cm

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