A rectangle of area 350 square feet is 14 times as wide as it is long. Find its length and width.

Solution:
1. Let the length of the rectangle be L.
2. Since the width is 14 times the length, the width is W = 14L.
3. The area of the rectangle is given by:
L \times W = 350

4. Substitute the expression for W in terms of L:
L \times 14L = 350

5. Simplify the equation:
14L^2 = 350

6. Divide both sides by 14 to solve for L^2:
L^2 = \frac{350}{14}
L^2 = 25

7. Take the square root of both sides:
L = \sqrt{25}
L = 5

8. Use the length to find the width:
W = 14L
W = 14 \times 5
W = 70

Therefore, the length of the rectangle is 5 feet, and the width is 70 feet.