The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 12 meters so the equation becomes: 2w + 2h = 12.

Putting these two equations together and solving for width (w):

2w + 2h = 12
w + h = \( \frac{12}{2} \)
w + h = 6
w = 6 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 6 - 2w
3w = 6
w = \( \frac{6}{3} \)
w = 2

Since h = 2w that makes h = (2 x 2) = 4 and the area = h x w = 2 x 4 = 8 m²

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,200
i = 0.05 x $1,200

No payments were made so the total amount due is the original amount + the accumulated interest:

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

To multiply terms with radicals, multiply the coefficients and radicands separately:

9\( \sqrt{6} \) x 2\( \sqrt{8} \)
(9 x 2)\( \sqrt{6 \times 8} \)
18\( \sqrt{48} \)

Now we need to simplify the radical:

18\( \sqrt{48} \)
18\( \sqrt{3 \times 16} \)
18\( \sqrt{3 \times 4^2} \)
(18)(4)\( \sqrt{3} \)
72\( \sqrt{3} \)

Betty scored 81% on the test meaning she earned 81% of the possible points on the test. There were 300 possible points on the test so she earned 300 x 0.81 = 243 points. Each question is worth 3 points so she got \( \frac{243}{3} \) = 81 questions right.