Answer:
2 cm and 6 cm
Step-by-step 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 ...
Only the first answer choice meets the requirement for a perimeter of 16 cm. The dimensions could be 2 cm and 6 cm.
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.
