# 9th grade (14y) + quadratic equation - examples

- MO Z8-I-1 2018

Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David. - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Pool

If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately? - Cuboid

Cuboid with edge a=6 cm and body diagonal u=35 cm has volume V=1980 cm^{3}. Calculate the length of the other edges. - Right triangle Alef

The area of a right triangle is 294 cm^{2}, the hypotenuse is 35 cm long. Determine the lengths of the legs. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Right triangle

Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle. - Rhombus and inscribed circle

It is given a rhombus with side a = 75 cm and the radius of the inscribed circle r = 36 cm. Calculate the length of its two diagonals. - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Tangents

To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. - 2nd class variations

From how many elements you can create 6972 variations of the second class? - Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - Trains

From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains. - RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments? - Perimeter and legs

Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm^{2}. - Cinema

Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium? - Tank

In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank? - Euler problem

Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels? - Rectangle diagonals

It is given rectangle with area 24 cm^{2}a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.

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