# 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.

Result

S = (Correct answer is: fr((5+sqrt(x/5))*x,2))

#### Solution:

$c_{1}=5 \ \text{cm} \ \\ h=x \ \\ c_{2}=\sqrt{ h/c_{1} }=\sqrt{ x/5 } \ \\ \ \\ c=c_{1}+c_{2} \ \\ \ \\ S=\dfrac{ c \cdot \ h }{ 2 } \ \\ S=\dfrac{ (5+\sqrt{ x/5 }) \cdot \ x }{ 2 }$

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