The area of a shape is the amount of space it can occupy.
- <em>The same hallway be painted with the same pattern, but using twice as much black paint as white paint</em>
- <em>The length of the hallway is 40 feet</em>
<em />
<em />
From the complete question (see attachment), the length of the white area is:
![\mathbf{Length = x + x + x + x + x}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D%20x%20%2B%20x%20%2B%20x%20%2B%20x%20%2B%20x%7D)
![\mathbf{Length = 5x}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D%205x%7D)
The width is:
![\mathbf{Width = 6}](https://tex.z-dn.net/?f=%5Cmathbf%7BWidth%20%3D%206%7D)
So, the area of the white segment is:
![\mathbf{Area = Length \times Width}](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D%20Length%20%5Ctimes%20Width%7D)
![\mathbf{Area = 5x \times 6}](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D%205x%20%5Ctimes%206%7D)
![\mathbf{Area = 30x }](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D%2030x%20%7D)
The length of the black area is:
![\mathbf{Length = x + 1 + x + 1 + x+1 +x +1}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D%20x%20%2B%201%20%2B%20x%20%2B%201%20%2B%20x%2B1%20%2Bx%20%2B1%7D)
![\mathbf{Length = 4x + 4}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D%204x%20%2B%204%7D)
The width is:
![\mathbf{Width = 6}](https://tex.z-dn.net/?f=%5Cmathbf%7BWidth%20%3D%206%7D)
So, the area of the black segment is:
![\mathbf{Area = Length \times Width}](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D%20Length%20%5Ctimes%20Width%7D)
![\mathbf{Area = (4x + 4) \times 6}](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D%20%284x%20%2B%204%29%20%5Ctimes%206%7D)
![\mathbf{Area = 24x + 24}](https://tex.z-dn.net/?f=%5Cmathbf%7BArea%20%3D%2024x%20%2B%2024%7D)
So, their areas are:
--- white area
--- black area
<u>The paints</u>
The equation is given as:
![\mathbf{2 \times White = Black}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%20%5Ctimes%20White%20%3D%20Black%7D)
Substitute the areas
![\mathbf{2 \times 30x = 24x + 24}](https://tex.z-dn.net/?f=%5Cmathbf%7B2%20%5Ctimes%2030x%20%3D%2024x%20%2B%2024%7D)
![\mathbf{60x = 24x + 24}](https://tex.z-dn.net/?f=%5Cmathbf%7B60x%20%3D%2024x%20%2B%2024%7D)
Collect like terms
![\mathbf{60x - 24x = 24}](https://tex.z-dn.net/?f=%5Cmathbf%7B60x%20-%2024x%20%3D%2024%7D)
![\mathbf{36x = 24}](https://tex.z-dn.net/?f=%5Cmathbf%7B36x%20%3D%2024%7D)
Divide both sides by 36
![\mathbf{x = \frac 23}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%3D%20%5Cfrac%2023%7D)
Because x has a positive real value, then the <em>same hallway be painted with the same pattern, but using twice as much black paint as white paint</em>
<u>Length of the hallway</u>
To calculate the length of the hallway, we simply equate both areas;
![\mathbf{30x = 24x + 24}](https://tex.z-dn.net/?f=%5Cmathbf%7B30x%20%3D%2024x%20%2B%2024%7D)
Collect like terms
![\mathbf{30x - 24x = 24}](https://tex.z-dn.net/?f=%5Cmathbf%7B30x%20-%2024x%20%3D%2024%7D)
![\mathbf{6x = 24}](https://tex.z-dn.net/?f=%5Cmathbf%7B6x%20%3D%2024%7D)
Divide both sides by 6
![\mathbf{x = 4}](https://tex.z-dn.net/?f=%5Cmathbf%7Bx%20%3D%204%7D)
So, the length of the hallway is the sum of the following lengths:
![\mathbf{Length = 5x}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D%205x%7D)
![\mathbf{Length = 4x + 4}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D%204x%20%2B%204%7D)
So, we have:
![\mathbf{Length =5x + 4x + 4}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D5x%20%2B%204x%20%2B%204%7D)
![\mathbf{Length =9x + 4}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D9x%20%2B%204%7D)
Substitute 4 for x
![\mathbf{Length =9 \times 4 + 4}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D9%20%5Ctimes%204%20%2B%204%7D)
![\mathbf{Length =40}](https://tex.z-dn.net/?f=%5Cmathbf%7BLength%20%3D40%7D)
So, the length of the hallway is 40 feet
Read more about areas at
brainly.com/question/5688437
Answer:
the answer is in last picture
Answer: I believe it would be 9 feet tall.
Step-by-step explanation:
The statues shadow is 2 times larger than the childs shadow so you would multipy the childs height by 2
Area = length x width
area = 2 3/4 x 2/5
area = 1 1/10 feet :)
Answer:
a estimate of 376
Step-by-step explanation:
I counted all the students and added
/ estimate