Two plots of land have the same perimeter. One is a square of side 32 m and the other is rectangular whose length is 48 m. Which one is larger in the area and how much?
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Side of the square = 32m
Perimeter of the square = 4 × 32 m = 128 m
As given, that the perimeter of the square Is equal to the perimeter of the rectangle.
length of the rectangle = 48m
Perimeter = 2 ( l + b )
128m = 2 ( 48 + b ) m
128m = 96m + 2b
128 - 96 m = 2b
32 m = 2b
16m = b
Area of the square = Side × Side
= 32m × 32m = 1024 m²
Area of the rectangle = Length × Breadth
= 32m × 16m = 512m²
Difference of their areas = 1024m² - 512 m²
= 512m²
Therefore, the area of the square is greater than that of the rectangle by 512m².
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