Question

The altitude of a triangle is increasing at a rate of 2.5 centimeters/minute while the area of the triangle is increasing at a rate of 2.0 square

centimeters/minute. At what rate is the base of the triangle changing when the altitude is 8.5 centimeters and the area is 83.0 square
centimeters?
Your answer: ____
Hint: The area A of a triangle with base b and height his given by A=1/2 BH

Answer 1

The base of the triangle is increasing at a rate of 0.5 centimeters/minute. To solve this problem, we need to use the formula for the area of a triangle: A=1/2 bh. We know that the area is 83 cm², the altitude is 8.5 cm and the rate of change of the area is 2 cm²/min. So we can rearrange the formula to give A/(bH). So for our example, A/(2*8.5H)=83/(2*8.5*H)=83/(17H)=83/17H=0.5 cm/min.