A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions?

Answer 1

#6 × 2#

For the rectangle

Area is #12\ "cm"^2#
# ℓb = 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 +- sqrt(b^2 - 4ac))/(2a)#) to find #ℓ#
#ℓ = (-(-8) +- sqrt((-8)^2 - (4 × 1 × 12)))/(2 × 1)#
#ℓ = (8 +- sqrt(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.
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Answer 2

Let the length of the rectangle be ( l ) and the width be ( w ). Given that the area of the rectangle is ( 12 ) square centimeters and the perimeter is ( 16 ) centimeters, we can set up the following equations:

[ l \times w = 12 ] [ 2l + 2w = 16 ]

We can solve these equations simultaneously to find the possible dimensions of the rectangle. One possible set of dimensions is ( l = 4 ) centimeters and ( w = 3 ) centimeters. Another possible set of dimensions is ( l = 6 ) centimeters and ( w = 2 ) centimeters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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