Question

The area of a rectangle with a perimeter of 500 cm is modeled by the function A = 250l − l^2 where l is the length of the rectangle. Which is a reasonable domain for the context of this situation?

1. 0< l < 500
2. 0< l < 250
3. 0< l < 125
4. −250 < l < 250

Answer 1

the perimeter is 500 cm, meaning the width + width + length + length is 500 cm in this rectangle.

clearly, since their sum is 500 total, the length of any of the sides cannot be larger than 500, it has to be less to allow room for the other 3 sides. L < 500.

and the length cannot be 0 either, because if it's, then there's no rectangle :). L > 0

L < 500 and L > 0 0 < L < 500.

Answer 2

Option 2 -
`0<l<250`

Explanation:

Given : The area of a rectangle with a perimeter of 500 cm is modeled by the function
`A = 250l-l^2` where l is the length of the rectangle.

To find : Which is a reasonable domain for the context of this situation?

Solution :

A function modeled area of the rectangle is

`A = 250l-l^2`

Where, l is the length of the rectangle.

Domain is the complete set of possible values of independent variable.

We know that Area cannot be negative.

So, Put area equals to zero.

`250l-l^2=0`

`l(250l-l)=0`

`l=0,250l-l=0`

`l=0,l=250`

Which means the value of l lies between 0 and 250.

So, The domain of the situation is
`0<l<250`.

Therefore, Option 2 is correct.