Side lengths

In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.

Correct result:

a =  12 cm
b =  8 cm

Solution:

$$\begin{gathered} S={\displaystyle \frac{a\cdot v_a}{2}}={\displaystyle \frac{b\cdot v_b}{2}} \\ a\cdot v_a=b\cdot v_b \\ 6\cdot a=9\cdot b \\ a=4+b=12\text{ cm } \\ 6a-9b=0 \\ a-b=4 \\ a=12 \\ b=8 \end{gathered}$$

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