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.

Try another example

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!

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 v_c = 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 h_AB 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?