Question

Ali makes a rectangle shape from a thread
of 100 cm length. Find the maximum possible area of the rectangle ?​

Answer 1

Answer:

625cm^2

Explanation:

Because length plus breadth comes out to be50cm as perimeter is 100cm so 25 plus 25 makes 50 and also 25 multiply 25 makes 625 whichcan be the largest value

Answer 2

Length of the thread when made into a rectangle will become the Perimeter of the rectangle.

Let l, b are the length and breadth of the rectangle so formed.

According to the question,

Perimeter = 100 cm

⇒2 ( l + b) = 100

⇒ l + b = 50

⇒ l = 50 - b.

Now,

Area of the rectangle is,

A = lb

A = b ( 50 - b)

A = 50b - b²

For Maximum area,

A' = 0.

A' = d/db ( 50b - b²)

A' = 50 - 2b

For maximum area,

50 - 2b = 0

2b = 50

b = 25

Now, Length = 50 - b = 50 - 25 = 25

Breadth = b = 25.

Therefore, Maximum area of the rectangle is 25 * 25 = 625 sq.cm.