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 42 meters so the equation becomes: 2w + 2h = 42.

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

2w + 2h = 42
w + h = \( \frac{42}{2} \)
w + h = 21
w = 21 - h

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

w = 21 - 2w
3w = 21
w = \( \frac{21}{3} \)
w = 7

Since h = 2w that makes h = (2 x 7) = 14 and the area = h x w = 7 x 14 = 98 m²

The factors of 52 are [1, 2, 4, 13, 26, 52] and the factors of 40 are [1, 2, 4, 5, 8, 10, 20, 40]. They share 3 factors [1, 2, 4] making 4 the greatest factor 52 and 40 have in common.

The factors of a number are all positive integers that divide evenly into the number. The factors of 16 are 1, 2, 4, 8, 16.

To fill a 15 gallon tank exactly halfway you'll need 7\(\frac{1}{2}\) gallons of fuel. Each fuel can holds 1\(\frac{1}{2}\) gallons so:

cans = \( \frac{7\frac{1}{2} \text{ gallons}}{1\frac{1}{2} \text{ gallons}} \) = 5

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:

\( \sqrt{\frac{16}{36}} \)
\( \frac{\sqrt{16}}{\sqrt{36}} \)
\( \frac{\sqrt{4^2}}{\sqrt{6^2}} \)
\(\frac{2}{3}\)