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18 Jan 2018, 02:56
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
80% (01:53) correct
20%
(02:34)
wrong
based on 70
sessions
History
Date
Time
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Not Attempted Yet
If the perimeter of a certain rectangle is 76 and its area is 360 then what is the length of its shortest side?
(A) 12
(B) 18
(C) 20
(D) 36
(E) 40
(A) 12
(B) 18
(C) 20
(D) 36
(E) 40
18 Jan 2018, 05:36
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Bunuel
Perimeter . = 2(l+b) = 76
i.e. l+b = 38
Area = l*b = 360
:et's think of two numbers whose sum is 38 and whose products is 360 (Instead of making a quadratic equation and creating more difficulty for ourselves)
The numbers are 18 and 20
Smaller side = 18
Answer: Option B
18 Jan 2018, 05:44
Kudos
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I went about it as follows:
the shortest side is the largest when the rectangle with perimeter 76 is a square so:
76/4 = 19
meaning the answer for length a of the shortest side has to be a<19
--> A or B
A) if shortest side 12, then longest side is 26 (2x 12+ 2x 26 = 76)
B) if shortest side 18, then longest side is 20 (2x 18+ 2x 20 = 76)
12x26 = 312
18x20 = 360 --> B
the shortest side is the largest when the rectangle with perimeter 76 is a square so:
76/4 = 19
meaning the answer for length a of the shortest side has to be a<19
--> A or B
A) if shortest side 12, then longest side is 26 (2x 12+ 2x 26 = 76)
B) if shortest side 18, then longest side is 20 (2x 18+ 2x 20 = 76)
12x26 = 312
18x20 = 360 --> B
