Chapter 3: Q. 28 (page 288)

Use optimization techniques to answer the questions in Exercises 25–30.
Find the area of the largest rectangle that fits inside a circle of radius $4$ .

Short Answer

Expert verified

The area of the rectangle is $32$ .

Step by step solution

Step 1. Given Information.

Radius of circle is $4$ .

Step 2. Form an equation.

Let x be the length of the given rectangle.

From the given information,

Diameter $, = 4 \times 2$

$= 8$

Step 3. Use Pythagoras theorem to find x.

Using Pythagoras theorem,

$x^{2} + x^{2} = 8^{2} 2 x^{2} = 64 x^{2} = 32$

Step 4. Find the area of rectangle.

The area of the rectangle which fits inside the area of the circle is the area of the square.

$x^{2} = 32$

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Use optimization techniques to answer the questions in Exercises 25–30.
Find the area of the largest rectangle that fits inside a circle of radius $4$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Form an equation.

Step 3. Use Pythagoras theorem to find x.

Step 4. Find the area of rectangle.

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Use optimization techniques to answer the questions in Exercises 25–30.Find the area of the largest rectangle that fits inside a circle of radius 4.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Form an equation.

Step 3. Use Pythagoras theorem to find x.

Step 4. Find the area of rectangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Statistics

Calculus

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Use optimization techniques to answer the questions in Exercises 25–30.
Find the area of the largest rectangle that fits inside a circle of radius $4$ .