Answer:
4.02 meters.
Step-by-step explanation:
In the diagram, the length of the ladder is |AC|.
If the foot of the ladder is x meters from the base of the ladder
Then the distance of the ladder up the wall, AB=2x meters.
Using Pythagoras Theorem
[tex]|AC|^2=|AB|^2+|BC|^2\\4.5^2=(2x)^2+x^2\\4.5^2=4x^2+x^2\\20.25=5x^2\\$Divide both sides by 5\\x^2=20.25\div 5\\x^2=4.05\\x=\sqrt{4.05}=2.01 feet[/tex]
Therefore, the distance of the ladder up the wall,
AB=2 X 2.01 =4.02 meters.
Answer:
The ladder reaches 4.02m up the wall.
Step-by-step explanation:
Check the attachment for the diagram.
A right-angled triangle with is formed.
Hypotenuse is |AC|
Opposite sides are |AB| and |BC|.
Where x is the distance of the foot of the ladder from the wall.
We are required to find the distance |AB|
Applying Pythagora's Rule,
|AC|² = |AB|² + |BC|²
(4.5)² + (2x)² + x²
20.25 = 4x² + x²
20.25 = 5x²
Divide both sides by 5
x² = 20.25/5
x² = 4.05
Taking square roots of both sides
x = ±√4.05
We are only interested in the positive part, as we deal with distance.
= √4.05
x ≈ 2.01 to two decimal places.
The distance |AB| = 2x = 2×2.01 = 4.02m
