question_answer

  Prove that the area of the triangle BCE described on one side BC of a square ABCD as  base is one half of the area of the similar triangle ACF described on the diagonal AC as base.               OR ABC is a right triangle with right angle at C. Let BC = a, CA = b, AB = c and let p be the length of the perpendicular from C on AB. Prove that cp = ab.

Answer:

  is a square.  is described on side BC is similar to described on diagonal AC. Since ABCD is a square. Therefore,                        and [Diagonal =(side)] Now,    [Since and are equilateral. Therefore, they are equiangular (each angle being equal to 60°) and hence OR Since                                   [(common)              (each = 90°)]