Question

A person wants to create a vegetable garden and keeps the rabbits out by enclosing it with 100 feet of fencing. The area of the garden is giving by the function A (w) = (50-w) where w is the width (in feet) of the garden. Can the garden have an area of 700 ft^2?

Answer 1

The garden can not have area of 700ft^2

Explanation:

We are given equation for area as

`A(w)=w* (50-w)`

where

w is the width (in feet) of the garden

now, we are given area =700 ft^2

so, we can set area =700

and then we can solve for w

`w* (50-w)=700`

`50w-w^2=700`

`-w^2+50w-700=0`

now, we can use quadratic formula

`ax^2+bx+c=0`

`w=(-b\pm √(b^2-4ac))/(2a)`

we can compare and find a,b, and c

a=-1 , b=50 , c=-700

now, we can plug values

`w=(-50\pm √(50^2-4\left(-1\right)\left(-700\right)))/(2\left(-1\right))`

`w=25-5√(3)i,\:w=25+5√(3)i`

We can see that values of w is not real

so, w does not exists when area =700

so, The garden can not have area of 700ft^2