Polygons

1103021405

Level: 
A
A side of a rhombus is \( 35\,\mathrm{cm} \) long and the length of one of its diagonals is \( 56\,\mathrm{cm} \). Give the measure of the angle that the other diagonal makes with the side of the rhombus. Round the result to two decimal places.
\( 53.13^{\circ} \)
\( 38.94^{\circ} \)
\( 36.87^{\circ} \)
\( 106.26^{\circ} \)

1103021606

Level: 
A
In the rectangle \( ABCD \), \( a=6\,\mathrm{cm} \) and the radius of the circumcircle \( r=4\,\mathrm{cm} \) (see the picture). Find the measure of the angle between the diagonals of the rectangle. Round the result to two decimal places.
\( 82.82^{\circ} \)
\( 48.59^{\circ} \)
\( 97.18^{\circ} \)
\( 36.12^{\circ} \)

2000005510

Level: 
A
The lengths of the sides of the rectangular garden are in the ratio \(3:4\). The line connecting the centers of adjacent sides is \(25\,\mathrm{m}\) long (see the picture). How long will it take for the owner to till the whole garden if he digs over \(1\,200\,\mathrm{dm}^2\) per hour?
\(100\) hours
\(50\) hours
\(30\) hours
\(40\) hours

2010006705

Level: 
A
The perimeter of a rectangle is \(22\, \mathrm{cm}\). The diagonal of this rectangle is \(\sqrt{65}\, \mathrm{cm}\). Find the sides of the rectangle.
\(7\, \mathrm{cm}\) and \(4\, \mathrm{cm}\)
\(14\, \mathrm{cm}\) and \(8\, \mathrm{cm}\)
\(6\, \mathrm{cm}\) and \(5\, \mathrm{cm}\)
\(10\, \mathrm{cm}\) and \(1\, \mathrm{cm}\)