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:

m1=5 cm m2=15 cm m=m1+m2=5+15=20 cm k=m m1=20 5=10 cm=10 cm l=m m2=20 1510 317.3205m_{ 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=m1 m2=5 155 38.66038.66 cmh=\sqrt{ m_{ 1 } \cdot \ m_{ 2 } }=\sqrt{ 5 \cdot \ 15 } \doteq 5 \ \sqrt{ 3 } \doteq 8.6603 \doteq 8.66 \ \text{cm}

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