Donna is planning to replace the rug in her bedroom, which she drew on the grid below to represent her room. The longest side of her room is 9 feet. Her brother, Lance, has a larger room that is similar but a different size. What could the dimensions of his room be?Select one:a.Lance's room could be 11 ft by 9 ft.b.Lance's room could be 13.5 ft by 9 ft.c.Lance's room could be14.5 ft by 10.5 ft.d.Lance's room could be 15 ft by 12 ft.
Question
Donna is planning to replace the rug in her bedroom, which she drew on the grid below to represent her room. The longest side of her room is 9 feet. Her brother, Lance, has a larger room that is similar but a different size. What could the dimensions of his room be?Select one:a.Lance's room could be 11 ft by 9 ft.b.Lance's room could be 13.5 ft by 9 ft.c.Lance's room could be14.5 ft by 10.5 ft.d.Lance's room could be 15 ft by 12 ft.
Solution
The question states that Lance's room is similar to Donna's room, which means the ratio of the lengths of the sides of the rooms must be the same. If Donna's longest side is 9 feet, then the dimensions of Lance's room must be a multiple of Donna's room dimensions.
Option a: 11 ft by 9 ft - This is not a multiple of Donna's room dimensions. Option b: 13.5 ft by 9 ft - This is not a multiple of Donna's room dimensions. Option c: 14.5 ft by 10.5 ft - This is not a multiple of Donna's room dimensions. Option d: 15 ft by 12 ft - This could be a possible dimension for Lance's room if Donna's room was 9 ft by 7.2 ft (since 15/9 = 12/7.2 = 1.67).
So, the correct answer is d. Lance's room could be 15 ft by 12 ft.
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