# Area of RT

Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.

Correct result:

S =  46.96

#### Solution:

$c=14 \ \\ c_{1}=5 \ \\ \ \\ c=c_{1}+c_{2} \ \\ v=\sqrt{ c_{1} \cdot \ c_{2} } \ \\ v=\sqrt{ c_{1} \cdot \ (c-c_{1}) }=\sqrt{ 5 \cdot \ (14-5) } \doteq 3 \ \sqrt{ 5 } \doteq 6.7082 \ \\ \ \\ S=\dfrac{ 1 }{ 2 } \cdot \ v \cdot \ c=\dfrac{ 1 }{ 2 } \cdot \ 6.7082 \cdot \ 14=21 \ \sqrt{ 5 }=46.96$

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