Q1
If a 30 meter ladder is placed against a wall such that it just reaches the top of the wall, if the horizontal distance between the wall and the base of the ladder is 1/3rd of the length of ladder, then the height of wall is:
Answer: B
Asked: the height of the wall.
The ladder, the wall and the ground form a right triangle. The ladder (30 m) is the hypotenuse.
Distance from the wall to the foot of the ladder = \( \frac{1}{3} \times 30 = 10 \) m.
By Pythagoras, height \( h = \sqrt{30^2 - 10^2} = \sqrt{900 - 100} = \sqrt{800} \).
\( \sqrt{800} = \sqrt{400 \times 2} = 20\sqrt{2} \) m (about 28.3 m).
Answer: \( 20\sqrt{2} \) metre