Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.

Therefore, the area of the circle inscribed into this triangle is

$1^{2} . π = π$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

The length of the sides of triangle are 3, 4, and 5.

Step 2: What is the area of the largest ellipse you can inscribe into a triangle.

We know that the largest ellipse that can be inscribed into any kind of triangle is a circle.

Same applies particularly for right triangles, as well.

We also know that,

For any kind of triangle with side lengths a,b, and c, if r is the radius of the circle inscribed into the triangle, and $s = \frac{a + b + c}{2}$ , then for the triangle's area applies $p = r s$ , which leads to $r = \frac{s}{p}$ .

A triangle with side lengths 3, 4, and 5 is a right triangle, so we have

$r = \frac{\frac{3 + 4 + 5}{2}}{\frac{3.4}{2}} r = \frac{6}{6} r = 1,$

So, the area of the circle inscribed into this triangle is

$I^{2} . π = π$ .

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Linear Algebra With Applications

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Short Answer

What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.

Step by Step Solution

Step 1: Given

Step 2: What is the area of the largest ellipse you can inscribe into a triangle.

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Linear Algebra With Applications

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What is the area of the largest ellipse you can inscribe into a triangle with side lengths 3,4 , and 5 ? Hint: The largest ellipse you can inscribe into an equilateral triangle is a circle.

Step by Step Solution

Step 1: Given

Step 2: What is the area of the largest ellipse you can inscribe into a triangle.

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