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Math
GeometryElementary Geometry For College Students, 7e7th Edition

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Chapter A.5, Problem 39E
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
BuyFindarrow_forward

Elementary Geometry For College St...

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

In Exercises 37-39, c 2 = a 2 + b 2 .

In the right triangle, find a if b = a + 3     a n d     c = a + 4 .

To determine

To find:

To find a if b=a+3  and  c=a+4.

Explanation

Consider the following equation,

c2=a2+b2.

The diagrammetic representation is given below,

Substitute the values of b=a+3  and  c=a+4 in the above equation to get the following,

c2=a2+b2(a+4)2=a2+(a+3)2

Since (a+b)2=a2+2ab+b2 then the above equation the following,

(a+4)2=a2+(a+3)2a2+8a+16=a2+a2+6a+9a2+8a+16=2a2+6a+9a2+8a+16−2a2−6a−9=0−a2+2a+7=0

Then multiply the above equation by −1 on both sides to get the following,

−1(−a2+2a+7)=−1×0a2−2a−7=0

The general form of the quadratic equation is given below,

ax2+bx+c=0

Where a is the number multiplied by x2, b is the number multiplied by x, and c is the constant term.

Quadratic formula:

The solution for ax2+bx+c=0 when a≠0 is given below,

x=−b±b2−4ac2a…(1)

Compare the given equation with general equation by substituting x=a to get the following,

ax2+bx+c=0⇒x2−2x−7=0

Therefore,

a=1,b=−2  and  c=−7

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Problem 38E

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