A patient's room is 10 feet wide and 15 feet long. If all rooms are built to the same proportions, what is the length of a room that is 18 feet wide?

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Multiple Choice

A patient's room is 10 feet wide and 15 feet long. If all rooms are built to the same proportions, what is the length of a room that is 18 feet wide?

Explanation:
When dimensions scale up or down while keeping the same shape, every measurement grows by the same factor. The width increases from 10 feet to 18 feet, a factor of 18/10 = 1.8. Apply that to the length: 15 × 1.8 = 27 feet. You can also see this by keeping the width:length ratio constant (10:15 simplifies to 2:3), so length = (3/2) × width = (3/2) × 18 = 27 feet. The room 18 feet wide would be 27 feet long.

When dimensions scale up or down while keeping the same shape, every measurement grows by the same factor. The width increases from 10 feet to 18 feet, a factor of 18/10 = 1.8. Apply that to the length: 15 × 1.8 = 27 feet. You can also see this by keeping the width:length ratio constant (10:15 simplifies to 2:3), so length = (3/2) × width = (3/2) × 18 = 27 feet. The room 18 feet wide would be 27 feet long.

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