# Triangle KLM

In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm

Result

k =  10 cm
h =  8.66 cm

#### Solution:

$m_{ 1 }=5 \ \text{cm} \ \\ m_{ 2 }=15 \ \text{cm} \ \\ m=m_{ 1 }+m_{ 2 }=5+15=20 \ \text{cm} \ \\ k=\sqrt{ m \cdot \ m_{ 1 } }=\sqrt{ 20 \cdot \ 5 }=10 \ \text{cm}=10 \ \text{cm} \ \\ l=\sqrt{ m \cdot \ m_{ 2 } }=\sqrt{ 20 \cdot \ 15 } \doteq 10 \ \sqrt{ 3 } \doteq 17.3205$
$h=\sqrt{ m_{ 1 } \cdot \ m_{ 2 } }=\sqrt{ 5 \cdot \ 15 } \doteq 5 \ \sqrt{ 3 } \doteq 8.6603 \doteq 8.66 \ \text{cm}$

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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

Showing 0 comments:
Be the first to comment!

Tips to related online calculators
See also our right triangle calculator.
See also our trigonometric triangle calculator.

## Next similar math problems:

1. 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.
2. Right 24
Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
3. 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.
4. Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
5. Triangular pyramid
A regular tetrahedron is a triangular pyramid whose base and walls are identical equilateral triangles. Calculate the height of this body if the edge length is a = 8 cm
6. Triangle ABC
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.
7. 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.
8. 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.
9. Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m.
10. Height UT
How long is height in the equilateral triangle with a side b = 43?
11. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
12. Triangle P2
Can triangle have two right angles?
13. Parametric equation
Find the parametric equation of a line with y-intercept (0,-4) and a slope of -2.
14. Calculation
How much is sum of square root of six and the square root of 225?
15. Theorem prove
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?
16. Completing square
Solve the quadratic equation: m2=4m+20 using completing the square method
17. GP members
The geometric sequence has 10 members. The last two members are 2 and -1. Which member is -1/16?