Question

a rancher has a roll of fencing to enclose a rectangular area. the table shows how the area that the rancher can enclose with the fencing depends on the width of the rectangle.

width w (ft)	area a (ft²)
20	1,600
30	2,100

which quadratic equation gives the area a of the rectangle in square feet given its width in w feet?
a(w)=w² + 90w a(w)= - w² + 200w a(w)= - w² + 100w √
the rancher decides to make the width of the rectangle 40 ft. what is the area of the rectangle?
□ ft²

Explanation:

Step1: Identify the correct formula

We know the correct quadratic - formula for the area is $A(w)=-w^{2}+100w$.

Step2: Substitute $w = 40$

Substitute $w = 40$ into the formula $A(w)=-w^{2}+100w$.
$A(40)=-(40)^{2}+100\times40$.

Step3: Calculate the result

First, calculate $(40)^{2}=1600$. Then, $-(40)^{2}=-1600$. And $100\times40 = 4000$.
$A(40)=-1600 + 4000$.
$A(40)=2400$.

Answer:

$2400$