Answer:
[tex]\frac{10}{7}\approx 1.43\text{ m}[/tex].
Step-by-step explanation:
We have been given the length of a straight line ABC is 5 m. We are asked to find the length of AB, when [tex]AB:BC=2:5[/tex].
We can represent our given ration as:
[tex]\frac{AB}{BC}=\frac{2}{5}[/tex]
We can write above ratio in terms of AC as:
[tex]\frac{AB}{AB+BC}=\frac{2}{2+5}[/tex]
[tex]\frac{AB}{AC}=\frac{2}{2+5}[/tex]
Upon substituting [tex]AC=5[/tex], we will get:
[tex]\frac{AB}{5}=\frac{2}{7}[/tex]
[tex]\frac{AB}{5}*5=\frac{2}{7}*5[/tex]
[tex]AB=\frac{2*5}{7}[/tex]
[tex]AB=\frac{10}{7}=1.42857[/tex]
Therefore, the length of AB is [tex]\frac{10}{7}\approx 1.43\text{ m}[/tex].
