Planimetrics - math word problems - page 141 of 185
Number of problems found: 3688
- Shadow of tree
Miro stands under a tree and watches its shadow and shadow of the tree. Miro is 180 cm tall, and its shade is 1.5 m long. The tree's shadow is three times as long as Miro's shadow. How tall is the tree in meters? - 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. - 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? - 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 ratio 2:4. The length of the midline is 20. How long are the bases of a trapezoid? - 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. - 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 circumference 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 o - 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. - TV diagonal
A diagonal TV is 0.56 m long. How big is the television screen if the aspect ratio is 16:9? - Rectangle vs square
One side of the rectangle is 1 cm shorter than the side of the square. The second side is 3 cm longer than the side of the square. The square and rectangle have the same area. Calculate the length of the sides of a square and a rectangle. - Squares above sides
In a right triangle, the areas of the squares above its sides are 169, 25, and 144. The length of its longer leg is: - Plot plan scale
The square-shaped plot actually covers an area of 81 ares. Maybe draw it in the village plan on a scale of 1:200. What will be the length of the side on the plan? - 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 - Construct 8
Construct an analytical geometry problem where it is asked to find the vertices of a triangle ABC: The vertices of this triangle are points A (1,7), B (-5,1) C (5, -11). The said problem should be used the concepts of distance from a point to a line, rati - Similarity coefficient
In the triangle TMA, the length of the sides is t = 5cm, m = 3.5cm, and a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, and 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other. - Trapezium diagonals
It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC. - Thales
Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm, as shown. Calculate the depth of the hole. - Shadow and light
Nine meters height poplar tree has a shadow 16.2 meters long. How long does shadow have at the same time as Joe if he is 1,4m tall? - Rectangular triangles
The lengths of the corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the areas of these triangles? A smaller rectangular triangle has legs 6 and - Rhombus construction
Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it, touching all sides.
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