Maths. Section B1Applications of Derivatives

The maximum area (in m2) of the flower bed is:

An architect designs a garden in a circular shape with centre E and radius 50 m. There is a flower bed ABCD of rectangular shape inside the garden as shown in the figure. Suppose length and width of the flower bed are 2x and 2y meters respectively.

Based on above information answer the following question:

The maximum area (in m²) of the flower bed is:

Answer & explanation

Correct answer: option 3

The correct answer is option (3) → 5000

Length = $2x$

Width = $2y$

and,

$x^2+y^2=2500$ [Using Pythagoras]

A = Area of rectangle = length × width

$= 2x.2y$

$=4xy$

and,

$x^2+y^2=2500$

let's write,

$x^2+y^2=2500$ ⇒ let $x=\sqrt{2500}\cos θ,y=\sqrt{2500}\sin θ$

$A=4xy=4.(50\cos θ)(50\sin θ)=5000.\sin(2θ)$

$max(\sin 2θ)=1$

$⇒ Area = A=5000m^2$

Based on above information answer the following question:

The maximum area (in m²) of the flower bed is:

Answer & explanation

Correct answer: option 3

The correct answer is option (3) → 5000

Length = $2x$

Width = $2y$

and,

$x^2+y^2=2500$ [Using Pythagoras]

A = Area of rectangle = length × width

$= 2x.2y$

$=4xy$

and,

$x^2+y^2=2500$

let's write,

$x^2+y^2=2500$ ⇒ let $x=\sqrt{2500}\cos θ,y=\sqrt{2500}\sin θ$

$A=4xy=4.(50\cos θ)(50\sin θ)=5000.\sin(2θ)$

$max(\sin 2θ)=1$

$⇒ Area = A=5000m^2$