The area of a rectangular space is 128 square feet.
a. Find all the possible pairs of whole number dimensions in feet.
b. Explain which pair allows enough space for a car to park.
c. If the length of the space is x feet, how would you describ
e the width using the
area
and the length
a. What are pairs of factors of 128? Start with 2, 64.
b. Pick the two factors that would allow the needed space.
c. L * W = Area
W = Area/L
a. To find all the possible pairs of whole number dimensions in feet, we need to consider all the pairs of factors of the given area, 128 square feet.
The factors of 128 are 1, 2, 4, 8, 16, 32, and 64. Now, we can pair these factors as length and width.
Possible pairs of whole number dimensions in feet are:
- Length: 1 ft, Width: 128 ft
- Length: 2 ft, Width: 64 ft
- Length: 4 ft, Width: 32 ft
- Length: 8 ft, Width: 16 ft
- Length: 16 ft, Width: 8 ft
- Length: 32 ft, Width: 4 ft
- Length: 64 ft, Width: 2 ft
- Length: 128 ft, Width: 1 ft
b. To determine which pair allows enough space for a car to park, we need to consider the dimensions of the car and compare it with the dimensions of the possible pairs. Let's assume a typical car has dimensions of approximately 16 ft in length and 6 ft in width.
From the possible pairs listed above, the pair with dimensions that allow enough space for a car to park would be:
- Length: 16 ft, Width: 8 ft
c. If the length of the space is x feet, we can find the width using the area and the length. The formula for calculating the area of a rectangle is:
Area = Length x Width
If the area is 128 square feet and the length is x feet, we can solve for the width by rearranging the formula:
Width = Area / Length
In this case, the width would be: Width = 128 / x feet.