Answer:
25 feet
Explanation:
Let the ladder be 'H' feet long
Given;
Ladder touches the wall at a height = H - 5 feet
The distance from the foot of the ladder to the wall = H - 10 feet
now a right angles triangle is formed by the system,
where,
Ladder forms the hypotenuse of the triangle
Height of the wall is the perpendicular
and, distance at the base is the base of the triangle formed
Therefore,
from the Pythagoras theorem, we have
H² = ( H - 10 )² + ( H - 5 )²
or
H² = H² + 100 - 20H + H² + 25 - 10H
or
H² = 2H² + 125 - 30H
or
H² -30H + 125 = 0
on solving the quadratic equation, we get
H² + ( - 5H - 25H ) + 125 = 0
or
H ( H - 5 ) - 25 (H - 5) = 0
or
(H - 5) × (H - 25) = 0
therefore,
we have
H = 5 feet and H = 25 feet
now,
H = 5 is not possible as this length of the ladder will lead to the negative distance at the base and also, the height of the at the wall be zero
Hence,
the length of the ladder is 25 feet
