Line ratio division

We divided line AB into two parts in a ratio of 3:5. The longer part was 6 cm longer than the shorter part. How long was the whole line in cm?

Final Answer:

x =  24 cm

Step-by-step explanation:

$$\begin{gathered} (5-3)\cdot d=6 \\ 2d=6 \\ d=\frac{6}{2}=3 \\ d=3 \\ x=(3+5)\cdot d=(3+5)\cdot 3=24=24\text{cm} \\ \text{ Verifying Solution: } \\ a=3\cdot d=3\cdot 3=9\text{cm} \\ b=5\cdot d=5\cdot 3=15\text{cm} \\ X=a+b=9+15=24\text{cm} \\ Y=b-a=15-9=6\text{cm} \end{gathered}$$

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