Question

suppose you have 100 ft of string to rope off a rectangular section for a bake sale at a school fair. The function A= -x^2+50x gives the area of the section in square feet, where x is the width in feet. what width gives you the maximum area you can rope off? What is the maxium area? what is the range of the function?

Answer 1

HI!!

Answer 2

make a square

Answer 3

is that all @misty1212

Answer 4

yes
you want the math teacher explanation?

Answer 5

yes please @misty1212

Answer 6

the vertex of \(A= -x^2+50x\) is found by computing \(-\frac{b}{2a}\) which in your case it
\[-\frac{50}{2\times (-1)}=25\]

Answer 7

you have 100 feet of fence, each side should be 25 to maximize the area, i.e. it should be a square
this is more or less obvious, the rectangle with fixed perimeter has the largest area if you make it a square
a square is the most symmetric rectangle

Answer 8

thank you @misty1212

Answer 9

\[\color\magenta\heartsuit\]