Math Problem Statement

The altitude (i.e., height) of a triangle is increasing at a rate of 3 cm/minute while the area of the triangle is increasing at a rate of 3 square cm/minute. At what rate is the base of the triangle changing when the altitude is 7 centimeters and the area is 94 square centimeters?

Solution

To solve this problem, we'll need to use related rates in calculus. Here's the step-by-step process:

Step 1: Identify the given information.

  • The altitude hh of the triangle is increasing at a rate of dhdt=3\frac{dh}{dt} = 3 cm/min.
  • The area AA of the triangle is increasing at a rate of dAdt=3\frac{dA}{dt} = 3 square cm/min.
  • When ( h = 7 \

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Math Problem Analysis

Mathematical Concepts

Calculus
Related Rates

Formulas

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Theorems

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Suitable Grade Level

Advanced High School

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