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Q.

The length of a rectangular field is 8m and breadth is 2m. If a square field has the same perimeter as this rectangular field, the field with the greater area is ____.


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Detailed Solution

The length of a rectangular field is 8m and breadth is 2m. If a square field has the same perimeter as this rectangular field, the field with the greater area is square field.
Given that length of a rectangular field = 8 m and breadth of a rectangular field = 2 m.
According to the given condition,
Perimeter of the square field = Perimeter of the rectangular field
⇒4 × side = 2 × (l + b)
⇒4 × side = 2 × (8 + 2)
⇒4 × side = 2 × 10
⇒4 × side = 20
⇒side = 204
⇒side = 5
∴ Side of the square is 5 m.
Now, we will find the area of square field,
Area of a square = side × side
= 5 × 5
= 25
∴ Area of the square field is 25sq. m.
Now, we will find the area of the rectangular field,
Area of a rectangle = length × breadth
= 8 × 2
= 16sq.m
∴ Area of the rectangular field is 16sq. m.
Hence, the square field has a greater area that of rectangular field.
 
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