The length of the ladder is .
Further explanation:
Given:
It is given that the rate at which the ladder slides down from a vertical wall is , at the same time the bottom of the ladder is away from the wall horizontally and the horizontally sliding rate is .
Calculation:
Consider the vertical length that is from the bottom of the wall to the top of the ladder as .
Consider horizontal length from the bottom of the wall to the bottom of the ladder as .
Consider the length of the ladder as .
The top of the ladder is sliding down the wall that means the value of is decreasing with a rate of , so the rate is as follows:
The bottom of the ladder is sliding away the wall that means the value of is increasing with a rate of , so the rate is as follows:
The ladder and the wall form the right angled triangle in which is two sides the is the hypotenuse of the triangle.
So according to the Pythagoras theorem, “the sum of the squares of the two sides is equal to the square of the hypotenuse of the right angled triangle.”
Now apply the Pythagoras theorem in the given problem as follows,
…… (1)
Now differentiate equation (1) to find an equation that relates rates because the information is given in rates,
Divide the above equation by .
.....(2)
Substitute for , for and for in equation (2) to obtain the value of as follows:
So the vertical length that is from the bottom of the wall to the top of the ladder is .
Substitute for and for in equation (1) to obtain the length of the ladder as follows:
Therefore the length of the ladder is .
Learn more:
1. Problem on rules of transformation of triangles: brainly.com/question/2992432
2. Problem on the triangle to show on the graph with coordinates: brainly.com/question/7437053
3. Problem on equivalent expression in simplified form: brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Height and distance
Keywords: Angle, height, bottom, length, distance, triangle, 10 meters, ladder, hypotenuse, vertical, Pythagoras theorem, sliding, sliding, 0.375m/s.