Answer:
Therefore the top of the ladder moves up 4 ft.
Explanation:
Given that a 25 foot ladder incline against a wall. So the top of it is 20 feet high.
It forms a right angled triangle.
Here Altitude = 20 foot, hypotenuses= 25 feet
Let the base = x
We applying the Pythagorean Theorem
Altitude²+ base²= hypotenuses²
⇒20²+x²= 25²
⇒x²= 625-400
⇒x²= 225
⇒x=15 foot
The distance between the bottom of the ladder and wall is 15 feet.
Again given that, the ladder is moved so that ladder travels toward wall twice the distance that the top of the ladder moves up.
Consider the top of the ladder moves up y feet.
So, The bottom of the ladder moves towards wall = 2y.
(15-2y) feet is the distance between the wall and the bottom of the ladder.
And the top of the ladder is = (20+y)
Now base = 15-2y, altitude = 20+y and hypotenuse = 25
Applying Pythagorean Theorem,
(20+y)²+(15-2y)²=25²
⇒400+40y+y²+225-60y+4y²=625
⇒5y²-20y+625=625
⇒5y²-20y=0
⇒5y(y-4)=0
⇒y=0,4
y=0 does not make sense.
∴y=4 ft
Therefore the top of the ladder moves up 4 ft.
The highest height the top of the ladder got to is mathematically given as
H= 3.2 ft
Question Parameter(s):
A 25-foot ladder leans against a wall
so that it is 20 feet high at the top
Generally,The distance x is mathematically given as
20^2 = (12-2x)^2+(16+x)^2
Where
20^2=16^2+d^2
d=12 ft
Hence
400 = 144-48x+4x^2+256+32x+x^2
5x^2-16x=0
x=3.2 ft
In conclusion, the highest height is
H= 3.2 ft
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