Maths practice for 14 year olds - page 165 of 361

Number of problems found: 7217

Ski lift height
What height difference does the 2.5 km long ski lift overcome when the horizontal distance of the entry and exit station is 1200 meters?
Garden diagonal length
The garden has a square shape, and its area is 8,100 m². It will be divided by a sidewalk connecting the two opposite garden peaks. How long will this trail be?
Track surface fitting
The circular running track has a diameter of 130 meters. Can a rectangular surface with dimensions of 12 m and 50 m be grassed inside the circle?
Trip passenger calculation
Forty-eight people took part in the winning trip to Paris. There were 4 more family members than people who won the trip. People who did not win the trip but bought the trip from one of the winners were 6 less than half of the passengers on the bus. How m
Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
Sound speed calculation
Calculate the speed of sound in the air a) at a temperature of t = 20 °C b) at a temperature of t = 27 °C
Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
Hostel room calculation
Fifty-one students are accommodated in the tourist hostel in 15 four-bed and three-bedrooms. How many rooms are there if there are 2 spaces left after housing? a) There are four-bed rooms. b) There are three-bed rooms.
Bike cost
The father gave his son € 100 to buy a bicycle, which was 40% of the total amount of the bicycle. How much did the bike cost?
Triangle height construction
A. Construct ∆ABC such that c = 55 mm, α = 45 °, β = 60 °. B. Draw any acute triangle and construct its heights.
Sailing
Solve the following problem graphically. The fishing boat left the harbor early morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then, When she docked and reached the fishing grounds, she launched the n
Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.
Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
Fighter
A military fighter flies at an altitude of 10 km. The ground position was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the arm's length is 17 cm and the height of the base is 12 cm.
Specialist hiring probability
A private company will hire two IT specialists. Thomas is among the five registered candidates. What is the probability that he will not be accepted?
Hexagon area calculation
Calculate the area of a regular hexagon inscribed in a circle with a radius r = 7 cm.
Water mixing
We have 520 ml of hot water and 640 ml of water at 48 °C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65 °C?
TV tower
Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°.

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