Polygons

9000020910

Level: 
A
The perimeter of a rectangle is \(28\, \mathrm{cm}\). The diagonal of this rectangle is \(10\, \mathrm{cm}\). Find the sides of the rectangle.
\(8\, \mathrm{cm}\) and \(6\, \mathrm{cm}\)
\(7\, \mathrm{cm}\) and \(7\, \mathrm{cm}\)
\(9\, \mathrm{cm}\) and \(5\, \mathrm{cm}\)
\(7\, \mathrm{cm}\) and \(3\, \mathrm{cm}\)

9000121708

Level: 
A
Consider a square \(ABCD\) and a point \(E\) on the side \(BC\) such that the angle \( BAE\) has measure \(20^{\circ }\). The point \(F\) is on the side \(CD\) and the length of \(AF\) equals to the length of \(AE\) (i.e. the triangle \(AEF\) is isosceles with \(AF\) and \(AE\) of equal length). Find the measure of the angle \( AEF\).
\(65^{\circ }\)
\(45^{\circ }\)
\(50^{\circ }\)
\(70^{\circ }\)

9000121709

Level: 
A
Consider a rectangle \(ABCD\) of a special ratio between the length and the width: if \(E\), \(F\), \(G\) and \(H\) denote the midpoints of the sides \(AB\), \(BC\), \(CD\) and \(DA\), respectively, then the measure of the angle \( AEH\) is \(25^{\circ }\). Find the measure of the angle \( EFG\).
\(50^{\circ }\)
\(65^{\circ }\)
\(75^{\circ }\)
\(130^{\circ }\)