Question

Justin made a scale drawing of a sailboat he saw at the harbor. The length of the actual boat is 24 feet, and the mast is 20 feet high. In Justin's sketch, the boat is 2 centimeters longer than the mast. What is the length of the boat on his sketch?

Answer 1

The length of the boat on his sketch is 12 cm

Answer 2

The length of the boat on his sketch is 12 centimeters.

To solve this problem, we need to determine the scale used in Justin's drawing based on the information given about the mast's height and then use that scale to find the length of the boat in the sketch.

1. Determine the scale:

- Actual mast height: 20 feet

- Sketch mast length: x centimeters (unknown)

- Sketch boat length: x + 2 centimeters (since the boat is 2 centimeters longer than the mast in the sketch)

2. Determine the scale ratio using the actual size and the sketch size. Since the actual size of the boat is 24 feet and the mast is 20 feet, we can set up a ratio comparing the two:

`\[ \text{Actual boat length : Actual mast height} = \text{Sketch boat length : Sketch mast length} \]`

`\[ 24\, \text{feet} : 20\, \text{feet} = (x + 2)\, \text{cm} : x\, \text{cm} \]`

Since 1 foot = 30.48 centimeters, we can convert feet to centimeters or vice versa. But in this case, we need the answer in centimeters, so we keep the ratio in feet to centimeters.

3. Solve for x using the proportion:

`\[ (24)/(20) = (x + 2)/(x) \]`

Now let's solve for x using this proportion.

The solution to the equation is x = 10 centimeters. This means that the mast in Justin's sketch is 10 centimeters high.

4. Find the length of the boat in the sketch:

Since the boat is 2 centimeters longer than the mast in the sketch, the length of the boat in Justin's sketch would be x + 2 centimeters.

`\[ \text{Length of the boat in the sketch} = 10\, \text{cm} + 2\, \text{cm} = 12\, \text{cm} \]`