Question

In a circular park of a diameter 80 there is a square shaped play ground of maximum area

Answer 1

Answer:

3200 units²

Step-by-step explanation:

To get the maximum area for the playground

⇒ the diagonal is the length of the diameter

Define x:

Let x be the length of the square

Find the length of the side of the square:

a² + b² = c²

x² + x² = 80²

2x² = 6400

x² = 3200

x = 40√2 units

Find the area of the playground:

Area = Length²

Area = (40√2)²

Area = 3200 units²

Answer: The maximum area of the playground is 3200 units²

Answer 2

Given:

Diameter = 80

To find:

Maximum area

Solution:

To find the length,

Length^2 + breadth^2 = area^2

As all sides are equal in a square,

2 ( Length )^2 = 6400

Hence,

Length = 40√2 units

Area = Length^2

(40√2)^2

Hence,

Area = 3200 sq.units