# All three dimensions of the lot. ### 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 82E
To determine

## To find: All three dimensions of the lot.

Expert Solution

All three dimensions of the lot are 168 ft, 175 ft and 49 ft.

### Explanation of Solution

Given:

The shape of a city lot is right triangle with perimeter 396 ft.

Hypotenuse of triangle is 7 ft longer than one of the other sides.

Calculation:

Let the one side of triangle be x.

Tabulate the given information into the language of algebra.

 In words In algebra One side of triangle x Hypotenuse of triangle x+7 Other side of triangle 392−(x+x+7)

Model the equation for the above information.

(Base)2+(height)2=(Hypotenuse)2x2+[392(2x+7)]2=(x+7)2

Simplify the above equation for x,

x2+(3852x)2=(x+7)2x2+148225+4x21540x=x2+14x+494x21554x+148176=0

Factor the above equation,

(2x441)(x168)=0x=4412,x=168

One side of right triangle is 168 ft.

Hypotenuse of triangle is,

x+7=168+7=175

Other side of triangle is,

392(2x+7)=392(2×168+7)=392343=49

Thus, all three dimensions of the lot are 168 ft, 175 ft and 49 ft.

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