TIFR CSE 2017 | Part A | Question: 8

Question

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?

• A. 3.90 inches
• B. $2 \sqrt{2}$ inches
• C. $2 \sqrt{3}$ inches
• D. 4.1 inches
• E. none of the above

Answer 1

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

also, AC²+AB² = BC² 

AC²+AB² = 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.

Answer 2

D. 4.1 inches

Theorem: Length of Perpendicular drawn to the hypotenuse can't be greater than half of length of hypotenuse.

Ref: https://goo.gl/CaL4sc