   Chapter 4.7, Problem 30E ### 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

# If the two equal sides of an isosceles triangle have length a, find the length of the third side that maximizes the area of the triangle.

To determine

To find: Length of the third side of the isosceles triangle so that it maximizes the area.

Explanation

Given: The two equal sides of an isosceles triangle have length a.

Solution:

Let the height of the isosceles triangle be h and base be b .

In Figure 1, AB is perpendicular on the base.

So, ABC be the right angle triangle.

Length of the BC be b2 .

In triangle ABC ,

sinθ=b2ab=2×a×sinθ

cosθ=hah=acosθ

Obtain the area of the triangle.

Z=12×b×h=12(2asinθ)(acosθ)=a2sinθcosθ=a22sin2θ

Differentiate Z with respect to θ .

dZdθ=a22×2cos2θ=a2cos2θ

For critical points, dZdθ=0

cos2θ =0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In problems 37-48, compute and simplify so that only positive exponents remain. 44.

Mathematical Applications for the Management, Life, and Social Sciences

#### True or False: is conservative.

Study Guide for Stewart's Multivariable Calculus, 8th

#### The absolute maximum value of f(x) = 6x − x2 on [1, 7] is: 3 9 76 −7

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