Side lengths

In the triangle ABC, the height to 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 answer:

a =  12 cm
b =  8 cm

Step-by-step explanation:

$$\begin{gathered} S=\frac{a\cdot v_a}{2}=\frac{b\cdot v_b}{2} \\ a\cdot v_a=b\cdot v_b \\ 6\cdot a=9\cdot b \\ a=4+b \\ 6a-9b=0 \\ a-b=4 \\ Row2-\frac{1}{6}\cdot Row1\to Row2 \\ 6a-9b=0 \\ 0.5b=4 \\ b=\frac{4}{0.5}=8 \\ a=\frac{0+9b}{6}=\frac{0+9\cdot 8}{6}=12 \\ a=12 \\ b=8 \end{gathered}$$

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