A ladder leans against a vertical wall. End of the ladder is 8 m above the ground. When the lower end of the ladder is moved 2 m farther away from the wall, the other end of the ladder rests against the foot of the wall. The length of the ladder is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 17 m
Against the wall, the ladder, the wall and the ground form a right triangle with the ladder as the hypotenuse. When the foot is pulled 2 m farther and the top comes down to the foot of the wall, the ladder lies flat on the ground, so its length equals the new distance of its foot from the wall.
Let the foot first be \(x\) m from the wall and the ladder be \(L\) m long:
Lying flat: \(L=x+2\) (1)
Against the wall: \(L^2=x^2+8^2\) (2)
Putting (1) in (2): \((x+2)^2=x^2+64\), so \(4x+4=64\) and \(x=15\)
\(L=15+2=17\) m