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

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

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

\( \frac{-3z^5}{4z^2} \)
\( \frac{-3}{4} \) z^{(5 - 2)}
-\(\frac{3}{4}\)z³

To add these radicals together their radicands must be the same:

8\( \sqrt{75} \) + 7\( \sqrt{3} \)
8\( \sqrt{25 \times 3} \) + 7\( \sqrt{3} \)
8\( \sqrt{5^2 \times 3} \) + 7\( \sqrt{3} \)
(8)(5)\( \sqrt{3} \) + 7\( \sqrt{3} \)
40\( \sqrt{3} \) + 7\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

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

\( \frac{27\sqrt{9}}{9\sqrt{3}} \)
\( \frac{27}{9} \) \( \sqrt{\frac{9}{3}} \)
3 \( \sqrt{3} \)