region 1 will require the most paint
Explanation:
length of tape = 24 ft
perimeter of the region to be painted = 24 ft
The region is rectangular, so we will apply the area of rectangle and perimeter to find the width.
perimeter = 2(length + width)
Area = length × width
We have 3 different regions with different lengths
For region 1:
length = 6 ft
from the formula for perimter, we can find the width:
perimeter = 2(length + width)
perimeter/2 = length + width
[tex]\text{width = }\frac{perimeter\text{ }}{2}-\text{ length}[/tex]
width for region 1 = 24/2 - 6 = 12 - 6
width = 6
Area = 6 × 6 = 36 ft²
For region 2:
length = 7 ft
width = 24/2 - 7 = 12 - 7
width = 5 ft
Area = 7 × 5 = 35 ft²
For region 3:
length = 8 ft
width = 24/2 - 8 = 12 - 8
width = 4 ft
Area = 8 × 4 = 32 ft²
b) The region that will require the most paint is the one that has the highest area. The higher the area, the larger the amount of paint that will be needed.
From calculations above, the highest area is 36 ft²
Hence, the region that will require the most paint is region 1
