A square field of side 25m and a rectangular field of length 28m have the same perimeter. Which field has a larger area?
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this is just an example showing that for a given perimeter, the square has the largest area.
p = 25*4 = 100
for rectangle, w = (100-2*28)/2 = 22
25^2 = 625
28*22 = 616
square is larger
To determine which field has a larger area, let's start by calculating the perimeter of each field and then comparing their areas.
1. Square Field:
Given: Side length = 25m
The perimeter of a square is found by multiplying the side length by 4.
Perimeter = 4 * 25m = 100m
The area of a square is calculated by squaring the side length.
Area = (25m)^2 = 625m²
2. Rectangular Field:
Given: Length = 28m
Let's assume the width is 'w' meters.
Given that the perimeter is the same, we can calculate it using the formula:
Perimeter = 2 * (Length + Width)
But since the length is given as 28m, we can plug it in and calculate the width:
100m = 2 * (28m + w)
Divide both sides by 2:
50m = 28m + w
Subtract 28m from both sides:
w = 50m - 28m
w = 22m
Now that we know the width of the rectangular field is 22m, we can calculate its area.
Area = Length * Width = 28m * 22m = 616m²
Comparison:
The square field has an area of 625m², while the rectangular field has an area of 616m².
Therefore, the square field has a larger area than the rectangular field.
To find out which field has a larger area between the square field and the rectangular field, we need to compare their areas.
1. Square field:
The formula to calculate the area of a square is A = side × side. In this case, the side of the square field is 25 meters. Therefore, the area of the square field is A = 25 × 25 = 625 square meters.
2. Rectangular field:
The perimeter of a rectangle can be calculated by using the formula P = 2(l + w), where l is the length and w is the width of the rectangle. In this case, the perimeter of the rectangular field is equal to the perimeter of the square field. So, we can set up the equation:
2(28 + w) = 4 × 25
Simplifying the equation:
56 + 2w = 100
2w = 100 - 56
2w = 44
w = 44/2
w = 22 meters
To calculate the area of the rectangular field, we use the formula A = length × width. In this case, the length is given as 28 meters and the width is 22 meters. So, the area of the rectangular field is A = 28 × 22 = 616 square meters.
Comparing the two areas, we find that the square field has an area of 625 square meters, while the rectangular field has an area of 616 square meters.
Therefore, the square field has a larger area than the rectangular field.