   Chapter A, Problem 30E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

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

# 29-32 Pythagorean Theorem These exercises require the use of the Pythagorean Theorem.The length of rectangle is 1   ft greater than its width. Each diagonal is 169   ft long. Find the dimension of the rectangle.

To determine

The dimensions of the rectangle.

Explanation

Given:

The length of rectangle is 1ft greater than its width.

Each diagonal is 169ft long.

Approach:

For a right angle triangle the Pythagorean Theorem is,

a2+b2=c2……(1)

Here, a is the perpendicular of the triangle, b is the base of the triangle, and c is the hypotenuse.

Calculation:

Let the width of the rectangle be xft.

Then, the length of the rectangle is x+1.

Substitute x for a, x+1 for b and 169 for c in equation (1), to calculate x.

(x)2+(x+1)2=(169)22x2+2x=28560x2+x14280=0x(x+120)119(x+120)=0

Simplify the above equation further

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