Question

If a 30 meter ladder is placed against a wall such that it just reaches the top of the wall, and the horizontal distance between the wall and the base of the ladder is 1/3rd of the length of ladder, then the height of the wall is:

A.
25 meter
B.
20\sqrt{2} meter
C.
20\sqrt{3} meter
D.
20 meter

Accepted Answer

B. Length of ladder (hypotenuse) $c = 30	ext{ m}$. Base $b = \frac{1}{3} 	imes 30 = 10	ext{ m}$. By Pythagoras theorem, $h^2 + b^2 = c^2$. $h^2 + 10^2 = 30^2 \implies h^2 = 900 - 100 = 800$. $h = \sqrt{800} = 20\sqrt{2}	ext{ m}$.

Ladder Against Wall Height Calculation

Explanation

Practise this under exam conditions