Question

I need the answer plsssss help guyss

Answer 1

Step-by-step explanation:

.

Let r be the radius of the circle and x metre be the length of each side of the square.

Then,

2πr+4x=28⇒πr+2x=14⇒r=

π

14−2x

……(i)

Let A be the combined area of the circle and the square. Then,

A=πr

2

+x

2

⇒A=π(

π

14−2x

)

2

+x

2

…..[Using (i)]

⇒A=

π

1

(14−2x)

2

+x

2

=

π

4

(7−x)

2

+x

2

dX

dA

=−

π

8

(7−x)+2x

and

dx

2

d

2

A

=

π

8

The critical numbers of A are given by

dx

dA

=0.

∴

dx

dA

=0

⇒−

π

8

(7−x)+2x=0

⇒x=

π+4

28

Clearly,

dx

2

d

2

A

=

π

8

>0 for all x.

Hence, A is minimum when x=

π+4

28

.

The lengths of two partions are 4x=

π+4

112

meter and,

28−

π+4

112

=

π+4

28π

m respectively.