Two plots of land have the same perimeter. Plot 1 is a square of side 128 m and the other plot 2 is a rectangle of length 128 m. The plot which has greater area is ____.

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Detailed Solution

Two plots of land have the same perimeter. Plot 1 is a square of side 128 m and the other plot 2 is a rectangle of length 128 m. The plot which has greater area is plot 1.
Given plot 1 is a square of side 128 m and the other plot 2 is a rectangle of length 128 m.
Perimeter of square is,
= 4 x Side
= 4 x 64
= 256 m
Now, perimeter of rectangle = 256 m.
Also, perimeter = 2(Length + Breadth)
256 = 2 (70 + b)
256 = 140 + 2b
2b = 256 – 140
2b = 116

b = 1162

b = 58 cm
Area of rectangle is,
= (length x breadth)
= (70 x 58) m²
= 4060 m²
Area of square,
= Side x Side
= (64 x 64) m²
= 4096 m².
So, plot 1 has a greater area.

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