In a circular park of diameter 80m there is a square shaped playground of maximum area the area of the plyaground is
Answers
Answer:
3200 m²
Step-by-step explanation:
Maximum area of a square formed is one with the diagonals equal to the diameter.
Define x:
Let the length of the sides be x
Find the length of the side of the square:
a² + b² = c²
x² + x² = 80²
2x² = 6400
x² = 3200
x = 40√2 m
Find the area:
Area = Length²
Area = (40√2)²
Area = 3200 m²
Answer: The maximum area is 3200 m²
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ALTERNATIVE METHOD:
Maximum area of a square formed is one with the diagonals equal to the diameter.
A square is a special rhombus with right angle.
⇒ Area of rhombus is 1/2 (diagonal 1 x diagonal 2)
Find Area of a square:
Area = 1/2 (diagonal 1 x diagonal 2)
Area = 1/2 ( 80 x 80) = 3200 m²
Answer: The maximum area is 3200 m²