Planimetry - math word problems - page 142 of 187
Number of problems found: 3735
- The spinner
The spinner below is spun 12 times. It landed on I 4 times, II 7 times, and III 1 time. What is the difference between the experimental and theoretical probabilities of landing on the II? - Isosceles trapezoid
In an isosceles trapezoid KLMN, the intersection of the diagonals is marked by the letter S. Calculate the area of the trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm². - Dimensions and area
Determine the actual dimensions of the kitchen and its area if its dimensions on the plan with a scale of 1:200 are 3.5 cm and 4 cm. - Bisector 2
ABC is an isosceles triangle. While AB=AC, AX is the bisector of the angle ∢BAC meeting side BC at X. Prove that X is the midpoint of BC. - Inequality triangle
The heel of height from the vertex C in the triangle ABC divides the side AB in the ratio 1:2. Prove that in the usual notation of the lengths of the sides of the triangle ABC, the inequality 3 | a-b | < c. - Shadow of tree
Martin stands under a tree and watches its shadow and shadow of the tree. Martin is 180 cm tall, and its shade is 1.5 m long. The tree's shadow is three times as long as Martin's shadow. How tall is the tree in meters? - MO Z9–I–2 - 2017
In trapezoid VODY, VO is the longer base. The diagonal intersection K divides segment VD in the ratio 3:2. The area of triangle KOV is 13.5 cm². Find the area of the entire trapezoid. - Angled cyclist turn
The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn? - Shadow
A 1-metre pole standing vertically on level ground casts a shadow 40 cm long. A nearby house casts a shadow 6 metres long at the same time. What is the height of the house? - Two 2
Two different harvesters together harvested potatoes from an area of 6.6 ha in one shift. The area that the less powerful harvester could harvest in six shifts, the more powerful one could harvest in five shifts. Determine the area that each harvester cou - Building shadow length
How long a shadow does a 15 m high building cast if a 1-metre-long vertical rod casts a shadow of 90 cm at the same time? Include a sketch showing the similarity. - The chimney
The chimney casts a shadow 45 meters long. The one-meter-long rod standing perpendicular to the ground has a shadow 90 cm long. Calculate the height of the chimney. - Geometry exercise
Calculations from geometry: The ratios of the sides of the quadrilateral are 3 : 6:4.5 : 3.5. Calculate their lengths if the perimeter is 51 cm. The sizes of the angles in the quadrilateral are equal to 29°30', 133°10', and 165°20'. What is the size of an - Wheel revolutions
The diameter of the motorcycle wheel is 60 cm. How many times does the wheel turn on a track 1,884 km long? - Two conductors
Two conductors have resistance Rs=5 ohms when connected in series and Rp=1.2 ohms when connected in parallel. Calculate the value of the resistors. - Proof PT
Can Pythagoras' theorem be easily proved using the Euclidean theorems? If so, do it. - The observer - trees
The observer sees the tops of two trees at the same angle α. It is 9 m from one tree and 21 m from the other. The trees stand on a level. How tall is the second tree if the height of the first is 6 m? Remember that the eyes of a standing person are approx - Area of RT
Calculate the area of a right triangle in which the hypotenuse has length 14 and one of the segments that the altitude creates on the hypotenuse has length 5. - Three altitudes
A triangle with altitudes 4, 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle. - Bases
The length of the bases trapezium is in the ratio 2:4. The length of the midline is 20. How long are the bases of a trapezoid?
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