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

Answer:

The garden can not have area of 700ft^2

Step-by-step explanation:

We are given equation for area as

$A(w)=w\times (50-w)$

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

$w\times (50-w)=700$

$50w-w^2=700$

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

now, we can use quadratic formula

$ax^2+bx+c=0$

$w=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

we can compare and find a,b, and c

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

now, we can plug values

$w=\frac{-50\pm \sqrt{50^2-4\left(-1\right)\left(-700\right)}}{2\left(-1\right)}$

$w=25-5\sqrt{3}i,\:w=25+5\sqrt{3}i$

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