The rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be the negative 8/3.
The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A 15-foot ladder is leaning against a wall of a house.
The base of the ladder is pulled away from the wall at a rate of 2ft/sec.
Then the equation will be
x² + y² = 15²
x² + y² = 225
Differentiate with respect to time. Then we have
2x (2) + 2yy' = 0
y' = -2x / y
Then the rate at which the area of the triangle is changing when the base of the ladder is 9 ft from the wall will be
Then the value of x will be
x² + 9² = 15²
x² + 81 = 225
x² = 144
x = 12 ft
Then the rate will be
y' = -2x / y
y' = – 2 × 12 / 9
y' = – 8/3
More about the differentiation link is given below.
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