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 result:

k =  10 cm
h =  8.6603 cm

Solution:

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

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

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