# The value of x . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.6, Problem 45E

(a)

To determine

## To find: The value of x.

Expert Solution

The value of x is 9 cm.

### Explanation of Solution

Given:

The given figure is, Figure (1)

The area of figure is 144cm2 .

Calculation:

Tabulate the given information into the language of algebra.

 In words In Algebra Length of part 1 x Area of part 1 10×x Width of part 2 x Area of part 2 6×x

Model the equation for the above information.

Areaofpart1+Areaofpart2=Totalarea10×x+6×x=144

Simplify the above equation for x,

10x+6x=14416x=144x=9

Thus, the value of x is 9 cm.

(b)

To determine

### To find: The value of x.

Expert Solution

The value of x is 5 in.

### Explanation of Solution

Given:

The given figure is, Figure (2)

The area of figure is 160in2 .

Calculation:

Tabulate the given information into the language of algebra.

 In words In Algebra Width of part 1 x Length of part 1 x+14 Area of part 1 x(x+14) Width of part 2 x Area of part 2 13×x

Model the equation for the above information.

Areaofpart1+Areaofpart2=Totalareax×(x+14)+13×x=160

Simplify the above equation for x,

x2+14x+13x=160x2+27x160=0(x+32)(x5)=0x=32,x=5

The value of x cannot be negative.

Thus, the value of x is 5 in.

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