A ladder rests against a wall. The top of the ladder touches the wall at height 12 metres. The length of the ladder is 4 metres longer than the distance from the base of the ladder to the wall. Find the length of the ladder.
Answers
Answer Expert Verified
Length of the ladder = sqrt (12^2 + 9^2) = sqrt (144 + 81) = sqrt 225 = 15. Therefore, if the ladder slips by 3 m, then the base becomes 12m. As the length of the ladder does not change, the ladder drops by the same amount, because of the above, Pythagoras Theorem, since 9^2 + 12^2 = 15^2.
Answer:
The correct answer is 16 metres.
Step-by-step explanation:
Given that, ladder rests against the wall.
Therefore the ladder, the wall and the base distance between the ladder and the wall will make a right angled triangle.
To find the length of the ladder, we will use pythagorus theorum.
It is given, length of the ladder is 4 metres longer than the distance from the base of the ladder to the wall.
And,
The top of the ladder touches the wall at height 12 metres.
Height of the wall (P) = 12 m
Let the base distance(B) be x.
Length of the ladder(H) = x + 4
According to Pythagorus Theorem,
H² = (P² + B²)
(x + 4)² = (12² + x²)
We know: (a+b)² = a² + b² + 2ab
x² + 16 + 8x = 144 + x²
8x = 144 - 16
x = 128/8
x = 16
Hence, the length of the ladder is 16m.
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