A prime number is an integer greater than 1 that has no factors other than 1 and itself. Examples of prime numbers include 2, 3, 5, 7, and 11.

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 48 meters so the equation becomes: 2w + 2h = 48.

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

2w + 2h = 48
w + h = \( \frac{48}{2} \)
w + h = 24
w = 24 - h

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

w = 24 - 2w
3w = 24
w = \( \frac{24}{3} \)
w = 8

Since h = 2w that makes h = (2 x 8) = 16 and the area = h x w = 8 x 16 = 128 m²

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

\( \frac{3}{9} \) ÷ \( \frac{4}{9} \) = \( \frac{3}{9} \) x \( \frac{9}{4} \)

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

\( \frac{3}{9} \) x \( \frac{9}{4} \) = \( \frac{3 x 9}{9 x 4} \) = \( \frac{27}{36} \) = \(\frac{3}{4}\)

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

4\( \sqrt{112} \) - 6\( \sqrt{7} \)
4\( \sqrt{16 \times 7} \) - 6\( \sqrt{7} \)
4\( \sqrt{4^2 \times 7} \) - 6\( \sqrt{7} \)
(4)(4)\( \sqrt{7} \) - 6\( \sqrt{7} \)
16\( \sqrt{7} \) - 6\( \sqrt{7} \)

Now that the radicands are identical, you can subtract them:

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{9}{36}} \)
\( \frac{\sqrt{9}}{\sqrt{36}} \)
\( \frac{\sqrt{3^2}}{\sqrt{6^2}} \)
\(\frac{1}{2}\)