Planimetrics - math word problems - page 144 of 185
Number of problems found: 3685
- Largest possible area
A right-angled triangle was inscribed in a circle with a diameter of 20 cm, whose hypotenuse is the circle's diameter and has the largest possible area. Calculate the area of this triangle. - Karim
Karim uses a photocopier to enlarge the triangle PQR diagram by 150%. a) Write the ratio of the length of P' Q' to the length of PQ. b) Is the ratio of the length P 'R' to the length PR equal to the ratio of the length P 'Q' to the length PQ? c) Use your - Shadow - an observation tower
How tall is the observation tower if it casts a shadow 9.6 m long at exactly the same moment that a half-meter pole casts a shadow 30 cm long? - 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-angl - Calculate 64444
The length of the linden shadow is 429 cm. The length of the shadow meter is 78cm. Calculate the height of the linden. - Vertex of the rectangle
Determine the coordinates of the vertex of the rectangle inscribed in the circle x²+y² -2x-4y-20=0 if you know that one of its sides lies on the line p: x+2y=0 - Vertical rod
The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long simultaneously. - Trapezoid - intersection of diagonals
In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate the trapezoid area. - 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? - 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? - Lookout tower
Calculate the height of a lookout tower forming a shadow of 36 m if a column 2.5 m high has a shadow of 1.5 m simultaneously. - Triangle
Prove whether you can construct a triangle ABC if a=8 cm, b=6 cm, c=10 cm. - 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. - 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? - Sides ratio
Calculate the circumference of a triangle with an area of 84 cm² if a:b:c = 10:17:21 - Parabolic 79764
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? - Selection 4
Selection triangle, which is similar to the given triangle RTG. ∆ RTG, r= 24 dm, t = 28 dm, g= 30 dm. ∆ SHV= 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= h= 7. - Quadrilateral in circle A quadrilateral is inscribed in the circle. Its vertices divide the circle in a ratio of 1:2:3:4. Find the sizes of its interior angles.
- Probability - triangles
We have five lines with lengths of 3cm, 5cm, 7cm, 9cm, and 11cm. What is the probability that we will be able to construct a triangle with randomly selected three? - Determine 82341
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1].
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