Triangle + system of equations - math problems

  1. Side lengths
    triangles_1 In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
  2. In a
    triangles_1 In a triangle, the aspect ratio a: c is 3: 2 and a: b 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
  3. An equilateral
    rs_triangle2 An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
  4. Conical bottle
    cone-upside When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
  5. Three parallels
    rs_triangle The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
  6. Sides of right angled triangle
    triangle_rt1 One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
  7. Faces diagonals
    cuboid_1 If the diagonals of a cuboid are x, y, and z (wall diagonals or three faces) respectively than find the volume of a cuboid. Solve for x=1.3, y=1, z=1.2
  8. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  9. Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  10. The second
    triangle The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
  11. Triangle 42
    triangle2_4 Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is measure of triangle BCA=?
  12. Isosceles triangle
    iso_tr_1 In an isosceles triangle, the length of the arm and the length of the base are in ration 3 to 5. What is the length of the arm?
  13. Rectangular triangle
    rt_triangle_2 The lengths of the rectangular triangle sides with a longer leg 12 cm form an arithmetic sequence. What is the area of the triangle?
  14. AP RT triangle
    right_triangle_4 The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
  15. Sphere from tree points
    sphere2_1 Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
  16. Three sides
    triangle_vysky_2 Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
  17. In a 2
    angles_7 In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
  18. Six-sided polygon
    hexagon-irregular In a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
  19. Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  20. Solid cuboid
    cuboid_18 A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.

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