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

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

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

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{450mi}{50mph} \)
9 hours

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

(\( \frac{28}{8} \) - \( \frac{6}{8} \)) cups
\( \frac{22}{8} \) cups
2\(\frac{3}{4}\) cups

If 34% of the town's 49,000 voters cast ballots the number of votes cast is:

(\( \frac{34}{100} \)) x 49,000 = \( \frac{1,666,000}{100} \) = 16,660

The mayor got 61% of the votes cast which is:

(\( \frac{61}{100} \)) x 16,660 = \( \frac{1,016,260}{100} \) = 10,163 votes.