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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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Chapter
Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Special Triangle Show that a right triangle whose sides are in arithmetic progression is similar to a 3 4 5 triangle.

To determine

To prove:

Right triangle with sides in arithmetic progression is similar to 345 triangle.

Explanation

Given:

A right triangle with sides in arithmetic progression.

Approach:

Use Pythagoras theorem and given information that sides are in arithmetic progression to relate the length of the sides and compare the lengths to a 345 triangle.

Calculation:

Sides are in arithmetic progression so we can assume the length of the sides are:

a,a+d,a+2d where a,d are both positive.

Now applying the Pythagoras theorem to this right triangle we get:

(a+2d)2=(a+d)2+a2a2+4d2+4ad=a2+d2+2ad+a24d2=a22ad+d2(2d)2=(ad)2

Case 1: a>d

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Chapter 13 Solutions

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