BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 7P
To determine

To find: The function that models area of equilateral triangle in terms of its length x of one of its sides.

Expert Solution

Answer to Problem 7P

The function that models area of given equilateral triangle is 34x2 .

Explanation of Solution

Draw the figure of equilateral triangle as shown below.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2, Problem 7P

Figure (1)

Area of triangle is,

A=12(base)(height)

The length of side of equilateral triangle is x .

In Figure (1) AD is median, it bisects CB so CD is x2 .

Use Pythagorean theorem in triangle ACD shown in Figure (1).

(AC)2=(CD)2+(AD)2

Substitute x for AC , x2 for CD in above equation.

(x)2=(x2)2+(AD)2x2=x24+AD2

Subtract x24 from both sides of above equation.

x2x24=AD234x2=AD2

Take square root of above equation and switch sides.

AD=34x

Summarize the all the information as shown in table below.

In Words In Algebra
Base x
Height 34x

Use the information in the table and model the function.

A=12(base)(height)=12(x)(34x)=12(x)(32x)=34x2

Thus, the function that models area of equilateral triangle is A(x)=34x2 .

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