If a rectangular room has a width of 10 ft and a length of 15 ft, and all rooms are built with the same proportions, what would be the length if the width is 18 ft?

• A. 27 ft
• B. 12 ft
• C. 23 ft
• D. 30 ft

Answer: (A)

Rectangles that are built with the same proportions have a constant length-to-width ratio. Here, the original room has length 15 and width 10, so the ratio length:width is 15:10, which simplifies to 3:2. If the width becomes 18, the length must scale by the same factor. Using the ratio, length = (3/2) × width. With width 18, length = (3/2) × 18 = 27. So the length is 27 ft.

The other options don’t keep the 3:2 ratio with a width of 18 (for example, 12 would give a 2:3 ratio, 23 isn’t 3:2 with 18, and 30 would give a 5:3 ratio).