Question

Jason plans to fence a rectangular area with 140 meters of fencing. He has written the formula A = w(70 - w) to express the area in terms of the width w. What is the maximum possible area enclosed with his fencing?

Answer 1

A=70w-w^2=-(w^2-70w+35^2)+35^2=-(w-35)^2+35^2
max or min occurs at the vertex, which is at (35,35^2), so the maximum occurs at x=35 and equals 35^2

Answer 2

\[A(w)=70w-w^2\] a parabola that opens down. max is at the vertex, and first coordinate of the vertex is \(-\frac{b}{2a}\)in your case it is \(-\frac{70}{-2}=35\)

Answer 3

so the answer is 1225 or 35? because when i solved 35^2 it equalled 35

Answer 4

but before you do any math at all, you should think
if you are going to make a rectangle with fixed perimeter and you want the area to be as large as possible, you should make a square

Answer 5

square as in box method?

Answer 6

a square as in a rectangle with 4 equal sides

Answer 7

ya 1225 is ans

Answer 8

right. sides should all be 35 and area is \(35^2\)

Answer 9

thnxx satellite

Answer 10

thanks everyone