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Write the area a of a square as a function of its perimeter p.
Solution:
Let ‘a’ be side of square and let ‘p’ be the perimeter then,
p = 4a
⇒ a = p/4
Area of square = a2
= (p/4)2
= p2/16
Therefore, the area ‘A’ of a square as a function of its perimeter ‘p’ is p2/16.
Example:
The perimeter of a square is 64 m. Find the area of the square.
Solution:
Perimeter of square = 64 m
Perimeter of square = 4 × side = 4 × 64
Side = 62/4 m = 16m
Now, the area of the square = (side × side)
Therefore,
Area of the square = 16× 16 m2 = 256 m2.
Using the relation
Area of square = p2/16
= 642/16
= 4096/16
= 256 m2
Write the area a of a square as a function of its perimeter p.
Summary:
The area ‘A’ of a square as a function of its perimeter ‘p’ is p2/16.
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