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Answer:
The area is changing at 15.75 square feet per second.
Step-by-step explanation:
The triangle between the wall, the ground, and the ladder has the following dimensions:
H: is the length of the ladder (hypotenuse) = 10 ft
B: is the distance between the wall and the ladder (base) = 6 ft
L: the length of the wall (height of the triangle) =?
dB/dt = is the variation of the base of the triangle = 9 ft/s
First, we need to find the other side of the triangle:
Now, the area (A) of the triangle is:
Hence, the rate of change of the area is given by:
Therefore, the area is changing at 15.75 square feet per second.
I hope it helps you!