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20 May 2016, 00:19
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
86% (00:58) correct
14%
(01:16)
wrong
based on 95
sessions
History
Date
Time
Result
Not Attempted Yet
What is the length of the diagonal of rectangle ABCD?
(1) The perimeter of the rectangle is 16.
(2) The area of the rectangle is 16.
(1) The perimeter of the rectangle is 16.
(2) The area of the rectangle is 16.
20 May 2016, 02:30
Kudos
Bookmarks
Bunuel
let x and y be the length and the width of the rectangle
the solution is to use pythagoras theorem to calculate the length of the diagonal of rectangle
using (1):
we have (x+y)*2 = 16 => x+y = 8 It tell nothing about the side of the rectangle => not sufficient
using (2):
we have x*y = 16 Still tell nothing about the side of the rectangle => not sufficient
combine (1) and (2):
we can calculate the side:
\(x + y = 8 => x = 8-y\)
\(x*y = 16\)
\(=> (8-y)*y=16\)
\(=>-y^2 + 8y = 16\)
\(=>-y^2 + 8y - 16 = 0\)
\((a = -1 ; b = 8; c = -16)\)
\(delta = b^2 - 4ac = 8^2 - 4*(-1)*(-16)\)
\(= 64 - 64 = 0\)
\(=> y = x = \frac{-b}{2a} =\frac{-8}{2*-1} = 4\)
=> the width and length of the rectangle will equal 4
=> we can use pythagoras theorem to calculate the length of the diagonal of rectangle
=> sufficient
=> answer is C
20 May 2016, 11:28
Kudos
Bookmarks
Bunuel
Question:- What is the length of diameter of length ABCD?
Diameter can be calculated if we know L and B. D= (L^2+B^2)^1/2
(1) The perimeter of the rectangle is 16.
2(L+B)= 16
L+B= 8----------- 1
L and B can have multiple values. Not sufficient
(2) The area of the rectangle is 16.
L*B= 16-----------2
L and B can have multiple values.
Combining statement 1 and 2. Put either value of L or B in any of the equations. We will get the answer.
C is the answer
