Answer: [tex]4x^{2}+80x-500=0[/tex]
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:
[tex]A=l*w[/tex]
Where [tex]l[/tex] is the lenght and [tex]w[/tex] is the width.
You have that the lenght and the width in feet are:
[tex]l=30\\w=10[/tex]
3. Let's call [tex]x[/tex] the width of the roped-off area. Then, the combined area is:
[tex]A_c=l_c*w_c[/tex]
Where
[tex]A_c=800[/tex]
[tex]l_c=l+x+x=30+2x[/tex]
[tex]w_c=w+x+x=10+2x[/tex]
4. Substitute values and simplify. Then:
[tex]800=(30+2x)(10+2x)[/tex]
[tex]800=300+60x+20x+4x^{2}\\4x^{2}+80x-500=0[/tex]
