The area of a rectangle is 80. What is the angle between the diagonal of the rectangle and its longer side?
1. The perimeter of the rectangle is 84
2. The shorter side of the rectangle is 2
Its easy to find from each statement that the longer side is 40 and the shorter is 2. However, how do we find the angle b/w the diagonal and the longer side? Are the angle measures formed by the diagonal of a rectangle fixed??? Thanks.
L*W = 80
2*(80/w + w)=84
w^2 -42w +80 =0
Factorizing, we get
(w-40)(w-2) = 0
w=40 or 2
Therefore, longer side is 40 and shorter is 2, which is easier part as you have mentioned. ( First, yes, the internal angles of a rectangle are 90deg But that wont help you much here)
Neither knowing that the diagonals of the rectangle are of equal length and they bisect each other.
Hmmm.....I am not sure how to proceed in a fast way.... If I could use Trigonometry, we can find the angle.
Anyways, as the angle can be found using both the statements ( i ) and ( ii ), the answer in GMAT DS should be "C".!
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