Another great question from the gmat club...

The theory behind this problem is very simple.

If one can calculate the ratios of the all the sides of a triangle, then one can always always always find the angles.You may ask how ?

Well, think about this

Let's say that Triangles ABC and DEF are similar.

AB/DE = BC/EF=AC/AF = say 1/2

Draw any triangle satisfying this equation and you will find that

Angle A = Angle D

Angle B = Angle E

Angle C = Angle FSo for the above question, We know the sides of the triangle (diagonal splits the triangle into 2. Additionally we can apply the Pythagoras to calculate the length of the triangle )

So if one were to draw a triangle with sides in the same ratio as that of the triangle(created when we drew the diagonal of the rectangle), then we can always derive the angles !

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