   Chapter 3.9, Problem 31E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area of the triangle increasing when the sides are 30 cm long?

To determine

To find: The rate of change of the area of an equilateral triangle.

Explanation

Given:

The rate of change of sides of an equilateral triangle is 10 cm/min.

Formula used:

(1) Chain rule: dydx=dydududx

(2). Area of an equilateral triangle of sides a:A=34a2 .

Calculation:

Let A be the area of the equilateral triangle and a be the length of each sides.

Since sides of the equilateral triangle are changes with time t. Therefore, area of the triangle become also changes with time t .

This means that area and sides of the triangle are function of the time t .

Differentiate A with respect to the time t .

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 