The area of a shape is the amount of space it can occupy.
From the complete question (see attachment), the length of the white area is:
[tex]\mathbf{Length = x + x + x + x + x}[/tex]
[tex]\mathbf{Length = 5x}[/tex]
The width is:
[tex]\mathbf{Width = 6}[/tex]
So, the area of the white segment is:
[tex]\mathbf{Area = Length \times Width}[/tex]
[tex]\mathbf{Area = 5x \times 6}[/tex]
[tex]\mathbf{Area = 30x }[/tex]
The length of the black area is:
[tex]\mathbf{Length = x + 1 + x + 1 + x+1 +x +1}[/tex]
[tex]\mathbf{Length = 4x + 4}[/tex]
The width is:
[tex]\mathbf{Width = 6}[/tex]
So, the area of the black segment is:
[tex]\mathbf{Area = Length \times Width}[/tex]
[tex]\mathbf{Area = (4x + 4) \times 6}[/tex]
[tex]\mathbf{Area = 24x + 24}[/tex]
So, their areas are:
[tex]\mathbf{Area = 30x }[/tex] --- white area
[tex]\mathbf{Area = 24x + 24}[/tex] --- black area
The paints
The equation is given as:
[tex]\mathbf{2 \times White = Black}[/tex]
Substitute the areas
[tex]\mathbf{2 \times 30x = 24x + 24}[/tex]
[tex]\mathbf{60x = 24x + 24}[/tex]
Collect like terms
[tex]\mathbf{60x - 24x = 24}[/tex]
[tex]\mathbf{36x = 24}[/tex]
Divide both sides by 36
[tex]\mathbf{x = \frac 23}[/tex]
Because x has a positive real value, then the same hallway be painted with the same pattern, but using twice as much black paint as white paint
Length of the hallway
To calculate the length of the hallway, we simply equate both areas;
[tex]\mathbf{30x = 24x + 24}[/tex]
Collect like terms
[tex]\mathbf{30x - 24x = 24}[/tex]
[tex]\mathbf{6x = 24}[/tex]
Divide both sides by 6
[tex]\mathbf{x = 4}[/tex]
So, the length of the hallway is the sum of the following lengths:
[tex]\mathbf{Length = 5x}[/tex]
[tex]\mathbf{Length = 4x + 4}[/tex]
So, we have:
[tex]\mathbf{Length =5x + 4x + 4}[/tex]
[tex]\mathbf{Length =9x + 4}[/tex]
Substitute 4 for x
[tex]\mathbf{Length =9 \times 4 + 4}[/tex]
[tex]\mathbf{Length =40}[/tex]
So, the length of the hallway is 40 feet
Read more about areas at
https://brainly.com/question/5688437
