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

Correct answer:

k =  10 cm
h =  8.6603 cm

Step-by-step explanation:

$$\begin{gathered} m_1=5\text{ cm } \\ {m}_2=15\text{ cm } \\ m=m_1+m_2=5+15=20\text{ cm } \\ k=\sqrt{m\cdot m_1}=\sqrt{20\cdot 5}=10\text{ cm } \\ l=\sqrt{m\cdot m_2}=\sqrt{20\cdot 15}=10\sqrt{3}\doteq 17.3205 \end{gathered}$$

$h=\sqrt{m_1\cdot m_2}=\sqrt{5\cdot 15}=5\sqrt{3}=8.6603\text{ cm}$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• Euclid theorems
  Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
• Euclid3
  Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg c_b = 39 cm.
• Median in right triangle
  In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
• Right triangle
  Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
• AP RT triangle
  The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
• RT perimeter
  The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
• 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
• Rectangular triangle PQR
  In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
• 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.
• Area of RT
  In the right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of ​​this triangle.
• Hypotenuse and height
  In a right triangle is length of the hypotenuse c = 56 cm and height h_c = 4 cm. Determine the length of both trangle legs.
• Right isosceles triangle
  Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
• Two diagonals
  The rhombus has a side length of 12 cm and a length of one diagonal of 21 cm. What is the length of the second diagonal?
• Right Δ
  A right triangle has the length of one leg 11 cm and the hypotenuse 61 cm size. Calculate the height of the triangle.
• Hypotenuse
  Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long.
• RT - hypotenuse and altitude
  Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
• KLM triangle
  Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.