Answer :
Answer:
Step-by-step explanation:
Area & Perimeter
The area is the product of a shape's side lengths.
Perimeter is the sum of all the side lengths of a shape.
In the case of a rectangle,
A = lw
P = 2l + 2w = 2(l + w)
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Solving the Problem
We're told that the area of a rectangle is 24.
So,
24 = lw.
If we want to find all the different perimeters that a rectangle with an area of 24 we just find how many different dimension combinations equal to an area of 24! (Excluding similar ones like 3 x 4 and 4 x 3).
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Why the Exclusion?
If we included all possible dimensions that give an area of 24, we'll have dimensions like 12 x 2 and 2 x 12.
If we find the perimeters of each we get
12 x 2:
P = 2(12 + 2) = 28
2 x 12:
P = 2(2 + 12) = 28.
They're the same so we must consider one of them, not both.
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There are
- 24 = 8 x 3
- 24 = 12 x 2
- 24 = 6 x 4
- 24 = 24 x 1
which is all the factors of 24.
Since there are 4 distinct combinations we'll have 4 different perimeters!
Verification:
8 x 3:
P = 2(8 + 3) = 22
12 x 2:
P = 28
6 x 4:
P = 2(6 + 4) = 20
24 x 1:
P = 2(24 + 1) = 50
All of the perimeters are distinct, there isn't two sets of dimensions that have perimeters equal to each other.
