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28 Aug 2026, 07:11
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B
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64%
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The length and width, in meters, of a rectangular swimming pool with a surface area of 2,160 square meters are both integers greater than 10. If the perimeter of the pool is p meters, what is the range of the set of possible values of p?
(A) 192
(B) 198
(C) 216
(D) 225
(E) 266
(A) 192
(B) 198
(C) 216
(D) 225
(E) 266
28 Aug 2026, 10:45
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Say:
- Length = a
- Breadth = b
a x b = 2160 = 6^3 x 10 = \(2^4\) x \(3^3\) x \(5^1\)
2160 -> expressed as product of two factors:
1 x 2160
2 x ...
.
.
10 x 216
12 x 180 (first example of a x b where both a and b are > 10)
.
.
45 x 48 (beyond this, we get the same numbers, with a and b reversed - 48 x 45, etc. till 2160 x 1).
p = 2(a+b)
To find max(p), max(a+b):
max(a+b) = 12+180 = 192.
To find min(p), min(a+b):
min(a+b) = 45+48 = 93
Final Solving:
Max(p) = 2 x 192 = 384
Min(p) = 2 x 93 = 186
Range(p) = 384 - 186 = 198. Choice B
---
Harsha
- Length = a
- Breadth = b
a x b = 2160 = 6^3 x 10 = \(2^4\) x \(3^3\) x \(5^1\)
2160 -> expressed as product of two factors:
1 x 2160
2 x ...
.
.
10 x 216
12 x 180 (first example of a x b where both a and b are > 10)
.
.
45 x 48 (beyond this, we get the same numbers, with a and b reversed - 48 x 45, etc. till 2160 x 1).
p = 2(a+b)
To find max(p), max(a+b):
max(a+b) = 12+180 = 192.
To find min(p), min(a+b):
min(a+b) = 45+48 = 93
Final Solving:
Max(p) = 2 x 192 = 384
Min(p) = 2 x 93 = 186
Range(p) = 384 - 186 = 198. Choice B
---
Harsha
30 Aug 2026, 04:58
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How would you quickly find the pair that mimimizes the perimeter ?
