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:

$$\begin{gathered} c_1=5\text{ cm } \\ h=x \\ {c}_2=\sqrt{h\mathrm{/}{c}_1}=\sqrt{x\mathrm{/}5} \\ c=c_1+c_2 \\ S={\displaystyle \frac{c\cdot h}{2}} \\ S={\displaystyle \frac{(5+\sqrt{x\mathrm{/}5})\cdot x}{2}} \end{gathered}$$

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