Question

application problems

1. boat builders share an old rule of thumb for sailboats. the maximum speed (k) in knots is about 1.35 times the square root of the length (l) in feet of the boats waterline. a customer is planning to order a sailboat with a maximum speed of 12 knots. how long should the waterline be?

Explanation:

⚡ Using what you learned: simplifying radical expressions

Step 1: Set up the equation

Using the given rule of thumb:

$$ K = 1.35\sqrt{L} $$

Substitute \( K = 12 \):

$$ 12 = 1.35\sqrt{L} $$

Step 2: Isolate the radical

Divide both sides by \( 1.35 \):

$$ \sqrt{L} = \frac{12}{1.35} $$

$$ \sqrt{L} \approx 8.8889 $$

Step 3: Solve for L

Square both sides to eliminate the radical:

$$ L = (8.8889)^2 $$

$$ L \approx 79.01 $$

Answer:

The waterline should be approximately \( 79 \) feet long (or about \( 79.01 \) feet).