R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.

Correct result:

S =  158.9 dm²

Solution:

$$\begin{gathered} c^2=a^2+b^2 \\ a=c-6 \\ a=b+3 \\ a>0 \\ b>0 \\ {b}^2-2\cdot 6\cdot b-2\cdot 6\cdot 3-6^2=0 \\ b=6+\sqrt{2\cdot 6^2+2\cdot 6\cdot 3}=16.39dm \\ a=b+3=19.39dm \\ S={\displaystyle \frac{1}{2}}ab={\displaystyle \frac{1}{2}}(b+3)b=158.9{\text{dm}}^2 \end{gathered}$$

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