Question

The area of a rectangle is 12 cm2. The lengths of its sides are natural numbers. Then, the perimeter of
the rectangle could be:​

Answer 1

Step-by-step explanation:

Explanation:

For the rectangle

Length

=

ℓ

Breadth

=

b

Area is

12

cm

2

ℓ

b

=

12

Perimeter is

16

cm

2

(

ℓ

+

b

)

=

16

ℓ

+

b

=

8

Substitute

b

=

12

ℓ

from first equation

ℓ

+

12

ℓ

=

8

ℓ

2

+

12

=

8

ℓ

ℓ

2

−

8

ℓ

+

12

=

0

Use quadratic formula (

x

=

−

b

±

√

b

2

−

4

a

c

2

a

) to find

ℓ

ℓ

=

−

(

−

8

)

±

√

(

−

8

)

2

−

(

4

×

1

×

12

)

2

×

1

ℓ

=

8

±

√

16

2

ℓ

=

8

±

4

2

ℓ

1

=

8

+

4

2

=

6

ℓ

2

=

8

−

4

2

=

2

If

ℓ

1

is taken as length then

ℓ

2

is the breadth of the rectangle.