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4 votes
4 votes

In a tutorial on geometrical constructions, the teacher asks a student to construct a right-angled triangle ABC where the hypotenuse BC is 8 inches and the length of the perpendicular dropped from A onto the hypotenuse is $h$ inches, and offers various choices for teh value of $h$. For which value of $h$ can such a triangle NOT exist?

  1. 3.90 inches
  2. $2 \sqrt{2}$ inches
  3. $2 \sqrt{3}$ inches
  4. 4.1 inches
  5. none of the above

2 Answers

Best answer
6 votes
6 votes

Area of the triangle is = 0.5*BC*h = 0.5*AB*AC

also, AC2+AB2 = BC2 

AC2+AB= 64

Since, AM>= GM

(AC2+AB2)/2 >= AC*AB

Hence, AC*AB <= 32

Therefore, area <= 16

Hence, 4*h <= 16

=> h <=4

Therefore, option (d) is correct.

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