A ladder is placed to reach a window 63 cm high. The ladder is then turned over to the opposite side of the street and is found to reach a point 56 cm high. If the ladder is 65 cm long, then the width of the street will be:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 49 cm
The foot of the ladder stays at one point of the street. On each side, the ladder, the wall and the ground form a right-angled triangle with the ladder as the hypotenuse, so Pythagoras' theorem gives the distance of the foot from each wall.
Towards the window: \(65^2-63^2=(65-63)(65+63)=2\times128=256\), so the foot is \(\sqrt{256}=16\) cm from this wall
Towards the other side: \(65^2-56^2=(65-56)(65+56)=9\times121=1089\), so the foot is \(\sqrt{1089}=33\) cm from that wall
The foot lies between the two walls, so the width of the street \(=16+33=49\) cm
