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A circular carpet is to be put on the rectangular floor of a living ro
[#permalink]
11 Aug 2025, 09:57
11 Aug 2025, 09:57
Expert Reply
00:00
Question Stats:
85% (01:26) correct
14% (01:23) wrong based on 14 sessions
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A circular carpet is to be put on the rectangular floor of a living room having the dimension of 12 feet \(\times\) 14 feet. What is the greatest diameter of the carpet that can be put on the floor, so that it is atleast 1 feet away from all the walls?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 11
(A) 6
(B) 8
(C) 9
(D) 10
(E) 11
A circular carpet is to be put on the rectangular floor of a living ro
[#permalink]
30 Aug 2025, 03:43
30 Aug 2025, 03:43
Expert Reply
The carpet must be at least 1 foot away from all the walls on the rectangular floor measuring 12 feet by 14 feet.
This means the carpet will be placed inside a smaller rectangle that is reduced by 1 foot on each side, both lengthwise and widthwise:
- Reduced length $\(=12-2 \times 1=10\)$ feet
- Reduced width $\(=14-2 \times 1=12\)$ feet
The carpet is circular, so the greatest diameter of the carpet is limited by the smaller dimension of this reduced rectangle, which is 10 feet.
Thus, the greatest diameter of the carpet that can be placed, while maintaining at least 1 foot distance from the walls, is 10 feet.
This means the carpet will be placed inside a smaller rectangle that is reduced by 1 foot on each side, both lengthwise and widthwise:
- Reduced length $\(=12-2 \times 1=10\)$ feet
- Reduced width $\(=14-2 \times 1=12\)$ feet
The carpet is circular, so the greatest diameter of the carpet is limited by the smaller dimension of this reduced rectangle, which is 10 feet.
Thus, the greatest diameter of the carpet that can be placed, while maintaining at least 1 foot distance from the walls, is 10 feet.
gmatclubot
A circular carpet is to be put on the rectangular floor of a living ro [#permalink]
30 Aug 2025, 03:43
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