Planimetry - math word problems - page 146 of 187
Number of problems found: 3735
- Exterior angles
In triangle ABC, the size of the exterior angle at vertex C is equal to 126°. The size of the internal angles at vertices A and B are in the ratio 5: 9. Calculate the size of the internal angles α, β, γ of triangle ABC. - Tree shadow
The tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time, a one-meter rod perpendicular to the horizontal surface has a shadow 64 cm long. How tall is the tree? - There
There is a stretched steel cable between the three columns. The height of the first column is 4 m, and the height of the second is 3.5 m. The distance between the first two columns is 2.5 m, and the distance between the second and third is 5 m. The heels - Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=100°. What sizes have other angles in a triangle? - Two similar triangles
Find unknown sides of a similar triangles: a = 6 cm, b = 8 cm, c =?, a '=?, b '= 12 cm, c' = 15 cm - Similar triangles
The triangles ABC and XYZ are similar. Find the unknown lengths of the sides of the triangles. The lengths: a = 5 cm, b = 8 cm and x = 7.5 cm z = 9 cm. - Trapezoid 83
Trapezoid ABCD is composed of five triangles. Points E and G divide segment AB in the ratio 2:4:3 (in this order) into three segments. Point F is the midpoint of segment AD. Triangle AEF is isosceles and right-angled. Triangles GBC and CDG are right-angle - Polygon 3
Polygon ABCD is dilated, rotated, and translated to form polygon QWER. The endpoints A and B are at (0, -7) and (8, 8), and the endpoints QW are at (6, -6) and (2, 1.5). What is the scale factor of the dilation? - Axial symmetry
Find the image A' of point A [1,2] in axial symmetry with the axis p: x = -1 + 3t, y = -2 + t (t = are a real number) - The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m? - Given are 3
Two statements are given: First statement: "If a quadrilateral is a parallelogram, then its diagonals bisect each other." Second statement: "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram." How many of the - Triangle side
The lengths of the sides of the triangle ABC are in the ratio 4:2:5. Calculate the size of the longest side of a similar KLM triangle, whose circumference is 66 cm. - Express the unknown
Using the formula p = F ÷ S, express the unknown F. - Tennis ball parabola
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court? - Triangle perimeter
In the ABC triangle, we connected the centers of the sides, creating a smaller triangle with a circumference of 14 centimeters. What is the perimeter of triangle ABC? - The shadow
The shadow of a 1 m high pole thrown on a horizontal plane is 0.8 m long. At the same time, the shadow of a tree thrown on a horizontal plane is 6.4 m. Determine the height of the tree. - Selection 4
Select the triangle that is similar to the given triangle RTG. △RTG: r = 24 dm, t = 28 dm, g = 30 dm. △SHV: s = 6 dm, h = 7.5 dm, v = 7 dm △VSH: v = 7 dm, s = 6 dm, h = 7.5 dm △HVS: h = 7.5 dm, v = 7 dm, s = 6 dm △VHS: v = 7 dm, h = 7.5 dm, s = 6 dm △HSV: - Similarity of two triangles
The KLM triangle has a side length of k = 6.3 cm, l = 8.1 cm, m = 11.1 cm. The triangle XYZ has a side length of x = 8.4 cm, y = 10.8 cm, z = 14.8 cm. Are triangle KLM and XYZ similar? (write 0. If not, if yes, find and write the coefficient of a similari - Arithmetic mean - parabola
Find the value of k so that k² + 2k – 3 is the arithmetic mean between k² + 4k + 5 and k² – 6k + 10. - Similar triangles
The triangles ABC and XYZ are similar. Find the unknown lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm
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