Question

A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions? 2 cm and 6 cm 3 cm and 4 cm 1.5 cm and 8 cm 1 cm and 12 cm

Answer 1

6

×

2

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.

Answer 2

2 cm and 6 cm

Explanation:

The product of the dimensions must be 12 cm². (All answer choices meet that requirement.)

Opposite sides of a rectangle are the same length, so the sum of the two dimensions must be half the perimeter, 8 cm. The sums of the answer choices are ...

• 8 cm
• 7 cm
• 9.5 cm
• 13 cm

Only the first answer choice meets the requirement for a perimeter of 16 cm. The dimensions could be 2 cm and 6 cm.