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 6 meters so the equation becomes: 2w + 2h = 6.

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

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

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

w = 3 - 2w
3w = 3
w = \( \frac{3}{3} \)
w = 1

Since h = 2w that makes h = (2 x 1) = 2 and the area = h x w = 1 x 2 = 2 m²

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

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

\( \frac{15\sqrt{32}}{3\sqrt{8}} \)
\( \frac{15}{3} \) \( \sqrt{\frac{32}{8}} \)
5 \( \sqrt{4} \)

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-2c⁶ x c³
(-2 x 1)c^{(6 + 3)}
-2c⁹

To divide fractions, invert the second fraction and then multiply:

\( \frac{2}{8} \) ÷ \( \frac{1}{8} \) = \( \frac{2}{8} \) x \( \frac{8}{1} \)

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{8} \) x \( \frac{8}{1} \) = \( \frac{2 x 8}{8 x 1} \) = \( \frac{16}{8} \) = 2