The length of a straight line ABC is 5 meters. The ratio of the length of AB to the length of BC is 2:5. Find the length of AB.

1. Problem Description

The length of a straight line ABC is 5 meters. The ratio of the length of AB to the length of BC is 2:

5. Find the length of AB.

2. Solution Steps

Let the length of AB be $x$ and the length of BC be $y$.

We are given that the length of the line ABC is 5 meters, which means:

$x + y = 5$

We are also given that the ratio of AB to BC is 2:5, which means:

$\frac{x}{y} = \frac{2}{5}$

From this, we can express $y$ in terms of $x$:

$y = \frac{5}{2}x$

Substitute this expression for $y$ into the first equation:

$x + \frac{5}{2}x = 5$

Multiply both sides of the equation by 2 to eliminate the fraction:

$2x + 5x = 10$

Combine the terms with $x$:

$7x = 10$

Divide both sides by 7 to solve for $x$:

$x = \frac{10}{7}$

Therefore, the length of AB is $\frac{10}{7}$ meters.

3. Final Answer

The length of AB is $\frac{10}{7}$ m.