Bunuel wrote:
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.
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