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

To fill a 20 gallon tank exactly halfway you'll need 10 gallons of fuel. Each fuel can holds 2\(\frac{1}{2}\) gallons so:

cans = \( \frac{10 \text{ gallons}}{2\frac{1}{2} \text{ gallons}} \) = 4

A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

37,000 fans x \( \frac{3}{4} \) = \( \frac{111000}{4} \) = 27,750 fans.

You have 20 out of the total of 250 raffle tickets sold so you have a (\( \frac{20}{250} \)) x 100 = \( \frac{20 \times 100}{250} \) = \( \frac{2000}{250} \) = 8% chance to win the raffle.

The amount of flour you need is (3\(\frac{1}{4}\) - \(\frac{1}{2}\)) cups. Rewrite the quantities so they share a common denominator and subtract:

(\( \frac{26}{8} \) - \( \frac{4}{8} \)) cups
\( \frac{22}{8} \) cups
2\(\frac{3}{4}\) cups