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 =  8.66 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 15=5 3=8.66 cmh=\sqrt{ m_{1} \cdot \ m_{2} }=\sqrt{ 5 \cdot \ 15 }=5 \ \sqrt{ 3 }=8.66 \ \text{cm}

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