Answer:
20 units
Explanation:
To find the smallest perimeter for a rectangular garden with an area of
24 square units, you want to find the dimensions that minimize the perimeter.
The formula for the perimeter (P) of a rectangle is given by:
P=2(length+width)
Given that the area (A) of the rectangle is 24 square units, you also know that:
A=length*width
In this case, A=24. You're looking for the dimensions that minimize the perimeter. The factors of 24 are:
1,2,3,4,6,8,12,24
Now, test these factors to find the pair that minimizes the perimeter. Consider:
1. 1×24gives P=2×(1+24)=2×25=50.
2. 2×12 gives P=2×(2+12)=2×14=28.
3. 3×8 gives P=2×(3+8)=2×11=22.
4. 4×6 gives P=2×(4+6)=2×10=20.
So, the pair (4,6) gives the smallest perimeter of 20 units. Therefore, for a rectangular garden with an area of 24 square units, the smallest perimeter is 20 units, and the dimensions are 4 units by 6 units.