Algebraic expressions, grade 9, question 12

27/01/2017 Grade 9

in the given figure: x>0  square,right triangle

BCDE is a square of side 2x, BAC is a right triangle at A s.t. AB = x.

  1. What is the nature of triangle ABC? Justify.
  2. Deduce the length of AC in terms of x.
  3. X represents the area of triangle ABC and Y represents that of square BCDE.
  4.  Express X and Y in terms of x.
  5. Can we find a value of x so that X = Y? Justify your answer.