the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate is the base b(t) chaging when the height h=15cm and the area A= 130cm2

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

(Eq. 1)

Where:

- Area of the triangle, measured in square centimeters.

- Base of the triangle, measured in centimeters.

- Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

(Eq. 2)

Where:

- Rate of change of area in time, measured in square centimeters per minute.

- Rate of change of base in time, measured in centimeters per minute.

- Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

(Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

If we know that , , and , the rate of change of the base of the triangle in time is:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.