question a triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant…

question a triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant. what is the rate of change of the area of the triangle if the height is 9 cm? provide your answer below: the rate of change of the area of the triangle is cm²/s.

question a triangle has a base that is decreasing at a rate of 11 cm/s with the height being held constant. what is the rate of change of the area of the triangle if the height is 9 cm? provide your answer below: the rate of change of the area of the triangle is cm²/s.

Answer

Explanation:

Step1: Recall area formula

The area formula of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Differentiate with respect to time

Since $h$ is constant, $\frac{dA}{dt}=\frac{1}{2}h\frac{db}{dt}$.

Step3: Substitute given values

We know that $h = 9$ cm and $\frac{db}{dt}=- 11$ cm/s. Substituting these values into the formula, we get $\frac{dA}{dt}=\frac{1}{2}\times9\times(-11)$.

Step4: Calculate the result

$\frac{dA}{dt}=\frac{9\times(-11)}{2}=-\frac{99}{2}=-49.5$ cm²/s.

Answer:

$-49.5$