# The range of values possible for the length of garden for fencing. ### 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 1.7, Problem 119E
To determine

## The range of values possible for the length of garden for fencing.

Expert Solution

The range of length of the garden for fencing is from 20 ft to 40 ft_.

### Explanation of Solution

The length of deer resistance fence is 120 ft and the area of the rectangular vegetable garden is atleast 800ft2.

Recall the fact that the value of perimeter of the garden will be equal to the length of the fence. That is, P=120 ft, A=800 ft2.

Since the area of the rectangular vegetable garden is atleast 800ft2, A800 ft2.

Note that, the perimeter of the rectangular vegetable garden is P=2(l+b) and the Area of the rectangular vegetable garden is A=(l×b) where l is the length and b breadth of the garden.

Substitute P=120 ft in P=2(l+b):

2(l+b)=120(l+b)=1202l+b=60b=60l

Substitute A800 ft2 in A=(l×b):

l×b800

Substitute b=60l in l×b800 as follows:

l×(60l)80060ll2800l260l800           [Multiplying by 1]l260l+(602)2800+(602)2l260l+900800+900

Simplify further as follows:

l260l+900800+900(l30)2100          (l30)2100|l30|1010l3010

Solve further as follows:

10+30l10+3020l40

Thus, the range of length of the garden for fencing is from 20 ft to 40 ft_.

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