Question

A roped-off area of width x is created around a 30- by 10-foot rectangular museum display of Native American artifacts. The combined area of the display and the roped-off area is 800 square feet. Whats an equation for the combined function

Answer 1

Answer:
`4x^(2)+80x-500=0`

Explanation:

1. You know that:

- The roped-off area whose width is represented with x, it is created around a rectangular museum.

- The dimensions of the rectangular museum are: 30 ft by 10 ft.

- The combined area of the display and the roped-off area is 800 ft².

2. The area of the rectangular museum can be calculated with:

`A=l*w`

Where
`l` is the lenght and
`w` is the width.

You have that the lenght and the width in feet are:

`l=30\\w=10`

3. Let's call
`x` the width of the roped-off area. Then, the combined area is:

`A_c=l_c*w_c`

Where

`A_c=800`

`l_c=l+x+x=30+2x`

`w_c=w+x+x=10+2x`

4. Substitute values and simplify. Then:

`800=(30+2x)(10+2x)`

`800=300+60x+20x+4x^(2)\\4x^(2)+80x-500=0`