# 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:

$t_{ 1 } = 8 \ cm \ \\ t_{ 2 } = 12 \ cm \ \\ \ \\ t_{ 1 }^2 = x^2 + (2y)^2 \ \\ t_{ 2 }^2 = y^2 + (2x)^2 \ \\ \ \\ x^2 = t_{ 1 }^2-4y^2 \ \\ \ \\ y = \sqrt{ \dfrac{ 4 \cdot \ t_{ 1 }^2-t_{ 2 }^2 }{ 15 } } = \sqrt{ \dfrac{ 4 \cdot \ 8^2-12^2 }{ 15 } } \doteq 2.7325 \ cm \ \\ x = \sqrt{ t_{ 1 }^2 - 4 \cdot \ y^2 } = \sqrt{ 8^2 - 4 \cdot \ 2.7325^2 } \doteq 5.8424 \ cm \ \\ \ \\ a = 2 \cdot \ x = 2 \cdot \ 5.8424 \doteq 11.6847 = 11.685 \ \text { cm }$
$b = 2 \cdot \ y = 2 \cdot \ 2.7325 \doteq 5.465 = 5.465 \ \text { cm }$
$a^2+b^2 = c^2 \ \\ \ \\ c = \sqrt{ a^2 + b^2 } = \sqrt{ 11.6847^2 + 5.465^2 } \doteq 12.8998 = 12.9 \ \text { cm }$

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...):

Be the first to comment!

#### Following knowledge from mathematics are needed to solve this word math problem:

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
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. Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
3. Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
4. Without Euclid laws
Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
5. Triangle ABC
Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
6. Goat and circles
What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
7. Right Δ
A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
8. Area of RT
Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
9. Tangents
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
10. Euklid4
Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
11. Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
12. Rectangle
In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
13. Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
14. Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
15. Area of RT
In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of ​​this triangle.
16. Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
17. RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?