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 24 meters so the equation becomes: 2w + 2h = 24.

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

2w + 2h = 24
w + h = \( \frac{24}{2} \)
w + h = 12
w = 12 - h

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

w = 12 - 2w
3w = 12
w = \( \frac{12}{3} \)
w = 4

Since h = 2w that makes h = (2 x 4) = 8 and the area = h x w = 4 x 8 = 32 m²

The commutative property states that, when adding or multiplying numbers, the order in which they're added or multiplied does not matter. For example, 3 + 4 and 4 + 3 give the same result, as do 3 x 4 and 4 x 3.

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

6\( \sqrt{75} \) - 2\( \sqrt{3} \)
6\( \sqrt{25 \times 3} \) - 2\( \sqrt{3} \)
6\( \sqrt{5^2 \times 3} \) - 2\( \sqrt{3} \)
(6)(5)\( \sqrt{3} \) - 2\( \sqrt{3} \)
30\( \sqrt{3} \) - 2\( \sqrt{3} \)

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

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

The number of students taking German or Spanish is 10 + 13 = 23. Of that group of 23, 4 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 23 - 4 = 19 who are taking at least one language. 27 - 19 = 8 students who are not taking either language.