Medians in right triangle

It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?

Result

a =  11.685 cm
b =  5.465 cm
c =  12.9 cm

Solution:

t1=8 cm t2=12 cm  t12=x2+(2y)2 t22=y2+(2x)2  x2=t124y2  y=4 t12t2215=4 82122152.7325 cm x=t124 y2=824 2.732525.8424 cm  a=2 x=2 5.842411.6847=11.685  cm t_{ 1 } = 8 \ cm \ \\ t_{ 2 } = 12 \ cm \ \\ \ \\ t_{ 1 }^2 = x^2 + (2y)^2 \ \\ t_{ 2 }^2 = y^2 + (2x)^2 \ \\ \ \\ x^2 = t_{ 1 }^2-4y^2 \ \\ \ \\ y = \sqrt{ \dfrac{ 4 \cdot \ t_{ 1 }^2-t_{ 2 }^2 }{ 15 } } = \sqrt{ \dfrac{ 4 \cdot \ 8^2-12^2 }{ 15 } } \doteq 2.7325 \ cm \ \\ x = \sqrt{ t_{ 1 }^2 - 4 \cdot \ y^2 } = \sqrt{ 8^2 - 4 \cdot \ 2.7325^2 } \doteq 5.8424 \ cm \ \\ \ \\ a = 2 \cdot \ x = 2 \cdot \ 5.8424 \doteq 11.6847 = 11.685 \ \text { cm }
b=2 y=2 2.73255.465=5.465  cm b = 2 \cdot \ y = 2 \cdot \ 2.7325 \doteq 5.465 = 5.465 \ \text { cm }
a2+b2=c2  c=a2+b2=11.68472+5.465212.8998=12.9  cm a^2+b^2 = c^2 \ \\ \ \\ c = \sqrt{ a^2 + b^2 } = \sqrt{ 11.6847^2 + 5.465^2 } \doteq 12.8998 = 12.9 \ \text { cm }

Try calculation via our triangle calculator.








Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Looking for help with calculating roots of a quadratic equation? Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation? Pythagorean theorem is the base for the right triangle calculator. See also our trigonometric triangle calculator.

Next similar math problems:

  1. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  2. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  3. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  4. Euclid 5
    euclid_3 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
  5. Catheti
    pyt_theorem The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
  6. Thunderstorm
    blesk The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
  7. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  8. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  9. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  10. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  11. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  12. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  13. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  14. Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  15. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  16. Square root 2
    parabola_2 If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
  17. Equation 23
    reciprocal_1 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)