A square and a rectangle have same perimeter. The length and breadth of the rectangle are 18cm and 14cm respectively. The area of the square is
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The side of a square with the same perimeter as a rectangle is always the arithmetic mean of the rectangle's length and breadth:
\[ s = \frac{l+b}{2} = \frac{18+14}{2} = 16\text{ cm} \]
Square Area \( = 16^2 = 256\text{ sq. cm}\). This provides a very fast shortcut!
Step 1: Calculate the rectangle's perimeter. Perimeter of rectangle = 2 x (length + breadth) = 2 x (18 + 14) = 2 x 32 = 64 cm. Step 2: Find the side of the square. The square has the same perimeter = 64 cm. Side of square = 64 / 4 = 16 cm. Step 3: Calculate the area of the square. Area = side^2 = 16 x 16 = 256 sq. cm. \[ \boxed{256} \]