   Chapter 5.4, Problem 22E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

A right triangle has legs of lengths x and 2x+2 and a hypotenuse of length 2x+3. What are the lengths of its sides?

To determine

To Find:

Lengths of the legs and hypotenuse of the triangle.

Explanation

Given A right triangle has legs of lengths x and 2x+2 and a hypotenuse of length 2x+3.

The figure can be redrawn as,

From the given data,

From the figure,

ABC is a right triangle,

BC is a hypotenuse and AB and AC are the legs of the triangle.

From the Pythagorean Theorem,

BC2=AB2+AC2(2x+3)2=(2x+2)2+x24x2+12x+9=4x2+8x+4+x212x+9=x2+8x+4x2

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