Question

Find the dimensions and maximum area of a rectangle if the perimeter is 52

Answer 1

Answer: l

=

16

,

b

=

10

Explanation:

Step-by-step explanation:

Perimeter of rectangle is  

p

=

2

(

l

+

b

)

=

52

,  

l

is length and  

b

is breadth.

Area of rectangle is  

A

=

l

⋅

b

=

160

∴

l

=

160

b

;

∴

2

(

160

b

+

b

)

=

52

or

(

160

b

+

b

)

=

26

or

160

+

b

2

b

=

26

or

160

+

b

2

=

26

b

or

b

2

−

26

b

+

160

=

0

or

b

2

−

16

b

−

10

b

+

160

=

0

or

b

(

b

−

16

)

−

10

(

b

−

16

)

=

0

or

(

b

−

16

)

(

b

−

10

)

=

0

∴

b

=

16

or

b

=

10

If  

b

=

16

;

l

=

160

16

=

10

and if  

b

=

10

;

l

=

160

10

=

16

The dimension of rectangle is  

l

=

16

,

b

=

10

[Ans]