Roger just got a puppy for his birthday. He and his mother will build a fence around an area in the backyard for the puppy to play in. The play area will be 24 square feet. What dimensions could the play area be? Which dimensions would require the least amount of fencing?
I'll be glad to check your answer.
To find the possible dimensions of the play area, we need to consider that the area is 24 square feet. The dimensions could be a combination of length and width that, when multiplied, equal 24.
We can start by listing the factors of 24:
1 x 24 = 24
2 x 12 = 24
3 x 8 = 24
4 x 6 = 24
So, the possible dimensions for the play area could be:
1. 1 ft x 24 ft
2. 2 ft x 12 ft
3. 3 ft x 8 ft
4. 4 ft x 6 ft
Now, to find the dimensions that require the least amount of fencing, we need to calculate the perimeter (total length of the fence required) for each set of dimensions.
The formula for the perimeter of a rectangle is P = 2 * (length + width).
For the dimensions:
1. P = 2 * (1 + 24) = 2 * 25 = 50 ft
2. P = 2 * (2 + 12) = 2 * 14 = 28 ft
3. P = 2 * (3 + 8) = 2 * 11 = 22 ft
4. P = 2 * (4 + 6) = 2 * 10 = 20 ft
From the calculations, we can see that the dimensions of 4 ft x 6 ft would require the least amount of fencing, with a perimeter of 20 ft.
Therefore, to minimize the amount of fencing required, Roger and his mother should build the play area with dimensions of 4 ft x 6 ft.