# 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:

$S=\dfrac{ a \cdot \ v_a }{ 2 }=\dfrac{ b \cdot \ v_b }{ 2 } \ \\ a \cdot \ v_a=b \cdot \ v_b \ \\ \ \\ \ \\ 6 \cdot \ a=9 \cdot \ b \ \\ a=4+b=12 \ \text{cm} \ \\ \ \\ 6a-9b=0 \ \\ a-b=4 \ \\ \ \\ a=12 \ \\ b=8$

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