Question

The perimeter of a rectangle is 200 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 900 square feet

Answer 1

ANSWER: The length (in feet) of a side is in the interval _____ or in the interval _____

Answer 2

let x be the width and y be the length of a rectangle in feet
the perimeter is made up of 2 lines of width and 2 of length so
2x+2y=200
now the area of the rectangle is given by
x*y<900

Answer 3

okay I get it so far

Answer 4

thinkinngg

Answer 5

the answers I got were 10 and 20 but those were wrong

Answer 6

okay so lets say
2y=200-2x
y=100-x
A=x*y
A=x*(100-x)
A=100x-x^2
900=100x-x^2

Answer 7

Now you are okay with all the Xs as long as they give a number below 900

Answer 8

so we have
900>=100x-x^2
x^2-100x+900>=0
(x -90)(x -10)>=0
x=90 or 10

which means y=10 or 90

Answer 9

now we have to see if x has to be greater than 90 or 10, or if it has to be less

Answer 10

200>=x>=90
these are the 2 intervals that will work out
0=<x=<10

Answer 11

would you like to see a graphical picture of this

Answer 12

How do you write these in interval notation?

Answer 13

umm

Answer 14

with brackets and stuff

Answer 15

http://www.wolframalpha.com/input/?i=A%3D100x-x%5E2

Answer 16

yeah

Answer 17

look at that btw, u can see how chosing x below 10, will result in less area, as well as chosing x greater than 90 is resulting is less area than 900