# Examples for 9th grade - page 46

- Distance runner

Distance runner already climbed three fifths of the total route. Thus passed 90 km. How many km he have to stop? How long is his route? - Three piles

100 kg of sugar we divide into three piles. The first pile is small. If we added to second 2 kg of sugar it would have 25% more sugar than the first pile. If we added to third pile 3 kg of sugar it would have 20% more sugar than the 2nd pile. How many kil - Rectangles - sides

One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm^{2}. What are the dimensions of the original rectangle? - Teams

How many ways can divide 16 players into two teams of 8 member? - Polygon 42

Which polygon has 42 more diagonals than sides? - Quadratic equation

Determine the numbers b, c that the numbers x_{1}= -1 and x_{2}= 3 were roots of quadratic equation: ? - Rectangle

The width of the rectangle is 65% of its length. Perimeter of the rectangle is 132 cm. Determine the dimensions of the rectangle. - Equilateral triangle v2

Equilateral triangle has a perimeter 36 dm. What is its area? - Right triangle trigonometrics

Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Cyclist

Cyclist rode two-fifths of the way the first day. The second day drove 5 km less while traveled three-eighths of route. How many kilometers does he have to finish target? - Two numbers

The sum of two numbers is 1. Identify this two numbers if you know that the half of first is equal to the third of second number. - Trapezoid thirds

The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment. - Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm. - Truck PRG-BA

Truck driving on highway from Prague to Bratislava at average speed of 72 km/h. At the moment when the truck passes 54 kilometer from Prague passenger car departs from Prague which travel to Bratislava at speed 90 km/h. When and where (at waht highway ki - Circle inscribed

Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm. - Cottages

The summer camp is 41 cottages. Rooms are for three and for four in them. How many of the 140 campers lives of three? - Cuboid - complicatef

Three walls of the same cuboid has content 6 cm^{2}, 10 cm^{2}and 15 cm^{2}. Calculate the volume of the cuboid. - Cube 7

Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm. - Silver medal

To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part? - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².

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