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13 Feb 2023, 23:51
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Difficulty:
15%
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Question Stats:
86% (01:56) correct
14%
(01:35)
wrong
based on 71
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A certain rectangle has an area of 48 and a perimeter of 32. What is the length of the diagonal of the rectangle?
A. 4
B. \(4\sqrt{3}\)
C. 16
D. \(4\sqrt{10}\)
E. 160
A. 4
B. \(4\sqrt{3}\)
C. 16
D. \(4\sqrt{10}\)
E. 160
14 Feb 2023, 07:43
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Bunuel
A certain rectangle has an area of 48 and a perimeter of 32. What is the length of the diagonal of the rectangle?
A. 4
B. \(4\sqrt{3}\)
C. 16
D. \(4\sqrt{10}\)
E. 160
\(lb = 48\) ; \(2(l +b) = 32\)A. 4
B. \(4\sqrt{3}\)
C. 16
D. \(4\sqrt{10}\)
E. 160
So, \(l + b = 16\)
Or, \(l = 16 - b\)
Thus, \(lb = 48 = (16 - b)b\)
Or, \(16b - b^2 = 48\)
Or, \(b^2 - 16b + 48 = 0\)
Or, \(b= 12 , 4\)
If \(b = 4\) ; \(l = 12\) (Possible as \(l > b\))
If \(b = 12\) ; \(l = 4\) (Not Possible as \(l < b\))
Thus, Diagonal will be \(\sqrt{4^2 + 12^2} = \sqrt{160}\) = \(4\sqrt{10}\), IMHO (D)
