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: $4x^{2}+80x-500=0$

Step-by-step 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:

 $800=(30+2x)(10+2x)$

$800=300+60x+20x+4x^{2}\\4x^{2}+80x-500=0$