Pythagorean theorem + system of equations - math problems

  1. 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.
  2. Cuboid
    cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
  3. Right triangle
    righttriangle Legs of right are in ratio a:b = 2:8. Hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
  4. R triangle
    right_triangle_1 Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
  5. Medians
    medias_triangle Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
  6. Rectangle SS
    rectangle Perimeter of a rectangle is 268 cm and its diagonal is 99.3 cm. Determine the dimensions of the rectangle.
  7. Circle
    kruznica Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
  8. Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  9. Trapezoid
    lichobeznik_3 trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
  10. Nice prism
    diagonal_rectangular_prism.JPG Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
  11. Diagonal 20
    plaza Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be?
  12. RT leg and perimeter
    rt_1 Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
  13. RTriangle 17
    rt The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
  14. Diamond diagonals
    kosostvorec_9 Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
  15. Isosceles trapezoid
    lichobeznik_5 Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high.
  16. Triangle - is RT?
    triangle_3_angles Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.
  17. Right angled triangle
    fun-triangle Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
  18. Rectangle
    diagonal_rectangle_2 The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
  19. Body diagonal
    kvader11_1 The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
  20. 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.

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