If Beth has 28 feet of trim to use as edging on a rectangular blanket, what is the length and width of two blanket sizes she could make?
what about a 7x7? or a 10x4? or a 8x6? or a 13x1?
3 by 4
To find the length and width of two blanket sizes Beth could make, you need to consider that the total length of the trim is 28 feet. Let's assume that the blanket has a length (L) and a width (W).
1. First case: Let's assume the length (L) is twice the width (W).
In this case, the perimeter of the blanket can be calculated as follows:
Perimeter = 2L + 2W
Since the trim is used as edging, it covers the entire perimeter of the blanket. Therefore:
Perimeter = 2L + 2W = 28 feet
Since we have an equation with two variables, we need to make an assumption to find the possible values.
Let's set an assumption for the width:
Assumption: W = 4 feet
Now we can solve the equation:
2L + 2W = 28
2L + 2(4) = 28
2L + 8 = 28
2L = 20
L = 10
Therefore, using the assumption W = 4 feet, one possible blanket size is L = 10 feet and W = 4 feet.
2. Second case: Let's assume the width (W) is three-quarters of the length (L).
Using the same logic as in the first case, we can set up the following equation:
Perimeter = 2L + 2W = 28 feet
Using this assumption:
Assumption: W = (3/4)L
Now we can solve the equation:
2L + 2W = 28
2L + 2(3/4)L = 28
2L + (6/4)L = 28
8L + 6L = 112
14L = 112
L = 8
Therefore, using the assumption W = (3/4)L, one possible blanket size is L = 8 feet and W = 6 feet.
So, two possible blanket sizes Beth could make are:
1. L = 10 feet, W = 4 feet
2. L = 8 feet, W = 6 feet