Pythagorean theorem + system of equations - examples

  1. Cuboid
    cuboid Cuboid with edge a=6 cm and body diagonal u=35 cm has volume V=1980 cm3. Calculate the length of the other edges.
  2. Right triangle
    righttriangle Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle.
  3. 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.
  4. 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.
  5. Rectangle SS
    rectangle Perimeter of a rectangle is 296 km and its diagonal is 104.74 km. Determine the dimensions of the rectangle.
  6. 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
  7. Circle
    circle_ag Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
  8. Trapezoid
    lichobeznik_3 trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
  9. 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.
  10. 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?
  11. 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.
  12. 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.
  13. Diamond diagonals
    kosostvorec_9 Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
  14. 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.
  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. 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.
  17. Rectangle
    diagonal_rectangle_2 The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
  18. 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?
  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. A bridge
    arc123 A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H

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Pythagorean theorem is the base for the right triangle calculator.